inquanto.computables

inquanto.computables.atomic

Submodule for quantum computable expressions that interact directly with InQuanto Protocols.

class ExpectationValue(state, kernel)

Bases: ComputableNode[float]

Represents the expectation value of a Hermitian operator kernel with a state.

\(\langle \Psi | H | \Psi\rangle\)

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the state \(|\Psi \rangle\).

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueBraDerivativeImag(state, kernel, symbols)

Bases: IExpectationValueDerivative

Represents the imaginary part of the bra derivatives of an expectation value of a Hermitian operator.

\(\Im \langle\partial_{\theta} \Psi(\theta) | H | \Psi(\theta)\rangle\)

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • kernel (QubitOperator) – Qubit operator kernel \(H\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the ansatz state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueBraDerivativeReal(state, kernel, symbols)

Bases: IExpectationValueDerivative

Represents the real part of the bra derivatives of an expectation value of a Hermitian operator.

\(\Re \langle \partial_{\theta} \Psi(\theta) | H | \Psi(\theta)\rangle\)

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • kernel (QubitOperator) – Qubit operator kernel \(H\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the ansatz state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueDerivative(state, kernel, symbols)

Bases: IExpectationValueDerivative

Represents the derivatives of the expectation value of a Hermitian operator.

\(\partial_{\theta} \langle \Psi(\theta) | H | \Psi(\theta) \rangle\)

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • kernel (QubitOperator) – Qubit operator kernel \(H\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the ansatz state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueKetDerivativeImag(state, kernel, symbols)

Bases: IExpectationValueDerivative

Represents the imaginary part of the ket derivatives of an expectation value of a Hermitian operator.

\(\Im \langle\Psi(\theta) | H | \partial_{\theta} \Psi(\theta)\rangle\)

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • kernel (QubitOperator) – Qubit operator kernel \(H\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the ansatz state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueKetDerivativeReal(state, kernel, symbols)

Bases: IExpectationValueDerivative

Represents the real part of the ket derivatives of an expectation value of a Hermitian operator.

\(\Re \langle\Psi(\theta) | H | \partial_{\theta} \Psi(\theta)\rangle\)

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • kernel (QubitOperator) – Qubit operator kernel \(H\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the ansatz state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueNonHermitian(state, kernel)

Bases: ComputableNode[complex]

Represents the expectation value of a non-Hermitian operator kernel with a state.

\(\langle \Psi | H | \Psi\rangle\)

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the state \(|\Psi \rangle\).

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: QubitOperator
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class MetricTensorImag(state, symbols)

Bases: IMetricTensor

Represents the imaginary part of the metric tensor.

Calculates: \(\Im \langle\partial_{\theta_i} \Psi(\theta) | \partial_{\theta_j}\Psi(\theta)\rangle\) for all \(i, j\).

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class MetricTensorReal(state, symbols)

Bases: IMetricTensor

Represents the real part of the metric tensor.

Calculates: \(\Re \langle\partial_{\theta_i} \Psi(\theta) | \partial_{\theta_j}\Psi(\theta)\rangle\) for all \(i, j\).

Parameters:

  • state (GeneralAnsatz) – Ansatz state \(|\Psi(\theta)\rangle\).

  • symbols (Set[Symbol]) – Symbols with respect to which the derivatives are computed.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in the state.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

state: GeneralAnsatz
symbols: Set[Symbol]
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class Overlap(bra_state, ket_state, kernel=<factory>)

Bases: IOverlap

Represents the overlap of two states with a Hermitian kernel operator.

\(\langle\Phi | H | \Psi\rangle\)

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

bra_state: GeneralAnsatz
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in both bra and ket states.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: Union[QubitOperator, QubitOperatorString]
ket_state: GeneralAnsatz
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class OverlapImag(bra_state, ket_state, kernel=<factory>)

Bases: IOverlap

Represents the imaginary part of the overlap of two states with a Hermitian kernel operator.

\(\Im \langle\Phi | H | \Psi\rangle\)

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

bra_state: GeneralAnsatz
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in both bra and ket states.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: Union[QubitOperator, QubitOperatorString]
ket_state: GeneralAnsatz
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class OverlapReal(bra_state, ket_state, kernel=<factory>)

Bases: IOverlap

Represents the real part of the overlap of two states with a Hermitian kernel operator.

\(\Re \langle\Phi | H | \Psi\rangle\)

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

bra_state: GeneralAnsatz
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in both bra and ket states.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: Union[QubitOperator, QubitOperatorString]
ket_state: GeneralAnsatz
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class OverlapSquared(bra_state, ket_state, kernel=<factory>)

Bases: IOverlap

Represents the overlap squared of two states with a kernel operator.

\(| \langle \Phi | P | \Psi \rangle |^2\)

Note

The kernel operator must be a single Pauli string.

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

bra_state: GeneralAnsatz
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns free symbols in both bra and ket states.

Return type:

Set[Symbol]

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

kernel: Union[QubitOperator, QubitOperatorString]
ket_state: GeneralAnsatz
label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

inquanto.computables.primitive

Primitive objects for constructing quantum computable expressions.

class ComputableFunction(func, *args)

Bases: ComputableNode[EvaluatedType]

Class representing a function applied to computable nodes in the expression tree.

Parameters:

  • func (Callable[..., TypeVar(EvaluatedType)]) – Callable expression to be evaluated.

  • args (Any) – Computable nodes passed to callable func.

Example

>>> from inquanto.computables.primitive import ComputableInt
>>> add = ComputableFunction(lambda x, y: x + y, ComputableInt(3), ComputableInt(4))
>>> result = add.evaluate()
>>> result
7
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

args: Tuple[Any, ...]
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Recursively evaluates the expression tree and returns the computed result.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – Evaluator function passed to the evaluate() methods of the child computable nodes recursively.

Returns:

Union[ComputableFunction, TypeVar(EvaluatedType)] – The computed result of the expression tree.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

func: Callable[..., TypeVar(EvaluatedType)]
is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableInt(value)

Bases: ComputableNode[int]

Computable wrapper class for an int, mainly for demonstration purposes.

Parameters:

value (int) – Integer value.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluates its value.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Any]], default: None)

Return type:

int

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

value: int
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableList(iterable=(), /)

Bases: list, ComputableNode[List]

Class representing a list of items of any types in the computable expression tree.

Parameters:

iterable – An iterable which produces elements to initialize the list.

Example

>>> from inquanto.computables.primitive import ComputableInt
>>> k_list = ComputableList([ComputableInt(1), ComputableInt(2), 3, "foo"])
>>> k_list
[ComputableInt(value=1), ComputableInt(value=2), 3, 'foo']
>>> len(k_list)
4
>>> k_list.evaluate()
[1, 2, 3, 'foo']
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

append(object, /)

Append object to the end of the list.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

clear()

Remove all items from list.

copy()

Return a shallow copy of the list.

count(value, /)

Return number of occurrences of value.

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluates each item in the list and returns the computed results as a list.

If an item is a computable, its evaluate() method is called. Otherwise, the item itself is returned.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Any]], default: None) – Callable passed to each item’s evaluate() method.

Returns:

Union[ComputableList, List] – The computed results of the items.

extend(iterable, /)

Extend list by appending elements from the iterable.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

index(value, start=0, stop=9223372036854775807, /)

Return first index of value.

Raises ValueError if the value is not present.

insert(index, object, /)

Insert object before index.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
pop(index=-1, /)

Remove and return item at index (default last).

Raises IndexError if list is empty or index is out of range.

print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

remove(value, /)

Remove first occurrence of value.

Raises ValueError if the value is not present.

reverse()

Reverse IN PLACE.

sort(*, key=None, reverse=False)

Sort the list in ascending order and return None.

The sort is in-place (i.e. the list itself is modified) and stable (i.e. the order of two equal elements is maintained).

If a key function is given, apply it once to each list item and sort them, ascending or descending, according to their function values.

The reverse flag can be set to sort in descending order.

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableNDArray(array_like: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], *args: Any, **kwargs: Any)

Bases: ndarray, ComputableNode[ndarray[Any, dtype[_ScalarType_co]]]

Class representing a multi-dimensional array of items in a computable expression tree.

This class dresses numpy ndarrays with Computable methods. It can contain computable items as objects, allowing computations to be deferred. It provides an interface to seamlessly integrate within a computational framework that uses Computable-based structures.

The array can be of any dimension, and its constructor signature is the same as a numpy array with the dtype set to object if a computable element is used. Supports all mathematical operations.

Parameters:

  • array_like – Initial data for the array. It can be a list, an already instantiated numpy array, or a list of Computable objects.

  • *args – Arguments passed to the numpy array constructor.

  • **kwargs – Key word arguments passed to the numpy array constructor, for example dtype=object

Example

>>> from inquanto.computables.primitive import ComputableInt
>>> qc_array = ComputableNDArray([ComputableInt(1), ComputableInt(2), ComputableInt(3), ComputableInt(4)], dtype=object)
>>> qc_array.evaluate()
array([1, 2, 3, 4], dtype=object)

>>> another_array = ComputableNDArray([ComputableInt(0), 1, ComputableInt(1), ComputableInt(0)])
>>> result = (qc_array + another_array)
>>> result.evaluate()
array([1, 3, 4, 4], dtype=object)

Note

The behavior of mathematical operations and functions on this class is determined by the behavior of the underlying numpy arrays. Computable items like ComputableInt will be evaluated when the evaluate() method is called.

T

View of the transposed array.

Same as self.transpose().

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.T
array([[1, 3],
       [2, 4]])

>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> a.T
array([1, 2, 3, 4])

See also

transpose

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

all(axis=None, out=None, keepdims=False, *, where=True)

Returns True if all elements evaluate to True.

Refer to numpy.all for full documentation.

See also

numpy.all

equivalent function

any(axis=None, out=None, keepdims=False, *, where=True)

Returns True if any of the elements of a evaluate to True.

Refer to numpy.any for full documentation.

See also

numpy.any

equivalent function

argmax(axis=None, out=None, *, keepdims=False)

Return indices of the maximum values along the given axis.

Refer to numpy.argmax for full documentation.

See also

numpy.argmax

equivalent function

argmin(axis=None, out=None, *, keepdims=False)

Return indices of the minimum values along the given axis.

Refer to numpy.argmin for detailed documentation.

See also

numpy.argmin

equivalent function

argpartition(kth, axis=-1, kind='introselect', order=None)

Returns the indices that would partition this array.

Refer to numpy.argpartition for full documentation.

Added in version 1.8.0.

See also

numpy.argpartition

equivalent function

argsort(axis=-1, kind=None, order=None)

Returns the indices that would sort this array.

Refer to numpy.argsort for full documentation.

See also

numpy.argsort

equivalent function

astype(dtype, order='K', casting='unsafe', subok=True, copy=True)

Copy of the array, cast to a specified type.

Parameters:

  • dtype (str or dtype) – Typecode or data-type to which the array is cast.

  • order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.

  • casting ({'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional) –

    Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.

    • ’no’ means the data types should not be cast at all.

    • ’equiv’ means only byte-order changes are allowed.

    • ’safe’ means only casts which can preserve values are allowed.

    • ’same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.

    • ’unsafe’ means any data conversions may be done.

  • subok (bool, optional) – If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.

  • copy (bool, optional) – By default, astype always returns a newly allocated array. If this is set to false, and the dtype, order, and subok requirements are satisfied, the input array is returned instead of a copy.

Returns:

arr_t (ndarray) – Unless copy is False and the other conditions for returning the input array are satisfied (see description for copy input parameter), arr_t is a new array of the same shape as the input array, with dtype, order given by dtype, order.

Notes

Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.

Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.

Raises:

ComplexWarning – When casting from complex to float or int. To avoid this, one should use a.real.astype(t).

Examples

>>> x = np.array([1, 2, 2.5])
>>> x
array([1. ,  2. ,  2.5])

>>> x.astype(int)
array([1, 2, 2])
base

Base object if memory is from some other object.

Examples

The base of an array that owns its memory is None:

>>> x = np.array([1,2,3,4])
>>> x.base is None
True

Slicing creates a view, whose memory is shared with x:

>>> y = x[2:]
>>> y.base is x
True
byteswap(inplace=False)

Swap the bytes of the array elements

Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.

Parameters:

inplace (bool, optional) – If True, swap bytes in-place, default is False.

Returns:

out (ndarray) – The byteswapped array. If inplace is True, this is a view to self.

Examples

>>> A = np.array([1, 256, 8755], dtype=np.int16)
>>> list(map(hex, A))
['0x1', '0x100', '0x2233']
>>> A.byteswap(inplace=True)
array([  256,     1, 13090], dtype=int16)
>>> list(map(hex, A))
['0x100', '0x1', '0x3322']

Arrays of byte-strings are not swapped

>>> A = np.array([b'ceg', b'fac'])
>>> A.byteswap()
array([b'ceg', b'fac'], dtype='|S3')
A.newbyteorder().byteswap() produces an array with the same values

but different representation in memory

>>> A = np.array([1, 2, 3])
>>> A.view(np.uint8)
array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
       0, 0], dtype=uint8)
>>> A.newbyteorder().byteswap(inplace=True)
array([1, 2, 3])
>>> A.view(np.uint8)
array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
       0, 3], dtype=uint8)
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

choose(choices, out=None, mode='raise')

Use an index array to construct a new array from a set of choices.

Refer to numpy.choose for full documentation.

See also

numpy.choose

equivalent function

clip(min=None, max=None, out=None, **kwargs)

Return an array whose values are limited to [min, max]. One of max or min must be given.

Refer to numpy.clip for full documentation.

See also

numpy.clip

equivalent function

compress(condition, axis=None, out=None)

Return selected slices of this array along given axis.

Refer to numpy.compress for full documentation.

See also

numpy.compress

equivalent function

conj()

Complex-conjugate all elements.

Refer to numpy.conjugate for full documentation.

See also

numpy.conjugate

equivalent function

conjugate()

Return the complex conjugate, element-wise.

Refer to numpy.conjugate for full documentation.

See also

numpy.conjugate

equivalent function

copy(order='C')

Return a copy of the array.

Parameters:

order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of a as closely as possible. (Note that this function and numpy.copy() are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)

See also

numpy.copy

Similar function with different default behavior

numpy.copyto

Notes

This function is the preferred method for creating an array copy. The function numpy.copy() is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.

Examples

>>> x = np.array([[1,2,3],[4,5,6]], order='F')

>>> y = x.copy()

>>> x.fill(0)

>>> x
array([[0, 0, 0],
       [0, 0, 0]])

>>> y
array([[1, 2, 3],
       [4, 5, 6]])

>>> y.flags['C_CONTIGUOUS']
True
ctypes

An object to simplify the interaction of the array with the ctypes module.

This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.

Parameters:

None

Returns:

c (Python object) – Possessing attributes data, shape, strides, etc.

See also

numpy.ctypeslib

Notes

Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):

_ctypes.data

A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as self._array_interface_['data'][0].

Note that unlike data_as, a reference will not be kept to the array: code like ctypes.c_void_p((a + b).ctypes.data) will result in a pointer to a deallocated array, and should be spelt (a + b).ctypes.data_as(ctypes.c_void_p)

_ctypes.shape

A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype('p') on this platform (see ~numpy.ctypeslib.c_intp). This base-type could be ctypes.c_int, ctypes.c_long, or ctypes.c_longlong depending on the platform. The ctypes array contains the shape of the underlying array.

Type:

(c_intp*self.ndim)

_ctypes.strides

A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.

Type:

(c_intp*self.ndim)

_ctypes.data_as(obj)

Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)).

The returned pointer will keep a reference to the array.

_ctypes.shape_as(obj)

Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short).

_ctypes.strides_as(obj)

Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong).

If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the as_parameter attribute which will return an integer equal to the data attribute.

Examples

>>> import ctypes
>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
>>> x
array([[0, 1],
       [2, 3]], dtype=int32)
>>> x.ctypes.data
31962608 # may vary
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
c_uint(0)
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
c_ulong(4294967296)
>>> x.ctypes.shape
<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
>>> x.ctypes.strides
<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
cumprod(axis=None, dtype=None, out=None)

Return the cumulative product of the elements along the given axis.

Refer to numpy.cumprod for full documentation.

See also

numpy.cumprod

equivalent function

cumsum(axis=None, dtype=None, out=None)

Return the cumulative sum of the elements along the given axis.

Refer to numpy.cumsum for full documentation.

See also

numpy.cumsum

equivalent function

data

Python buffer object pointing to the start of the array’s data.

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

diagonal(offset=0, axis1=0, axis2=1)

Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.

Refer to numpy.diagonal() for full documentation.

See also

numpy.diagonal

equivalent function

dot()
dtype

Data-type of the array’s elements.

Warning

Setting arr.dtype is discouraged and may be deprecated in the future. Setting will replace the dtype without modifying the memory (see also ndarray.view and ndarray.astype).

Parameters:

None

Returns:

d (numpy dtype object)

See also

ndarray.astype

Cast the values contained in the array to a new data-type.

ndarray.view

Create a view of the same data but a different data-type.

numpy.dtype

Examples

>>> x
array([[0, 1],
       [2, 3]])
>>> x.dtype
dtype('int32')
>>> type(x.dtype)
<type 'numpy.dtype'>
dump(file)

Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.

Parameters:

file (str or Path) –

A string naming the dump file.

Changed in version 1.17.0: pathlib.Path objects are now accepted.

dumps()

Returns the pickle of the array as a string. pickle.loads will convert the string back to an array.

Parameters:

None

evaluate(evaluator=None)

Evaluates each item in the array and returns the computed results as an array.

If an item is a computable, its evaluate() method is called. Otherwise, the item itself is returned.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Any]], default: None) – Callable passed to each item’s evaluate() method.

Returns:

Union[ComputableNDArray, ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – The computed results of the items.

fill(value)

Fill the array with a scalar value.

Parameters:

value (scalar) – All elements of a will be assigned this value.

Examples

>>> a = np.array([1, 2])
>>> a.fill(0)
>>> a
array([0, 0])
>>> a = np.empty(2)
>>> a.fill(1)
>>> a
array([1.,  1.])

Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:

>>> a = np.array([None, None], dtype=object)
>>> a[0] = np.array(3)
>>> a
array([array(3), None], dtype=object)
>>> a.fill(np.array(3))
>>> a
array([array(3), array(3)], dtype=object)

Where other forms of assignments will unpack the array being assigned:

>>> a[...] = np.array(3)
>>> a
array([3, 3], dtype=object)
flags

Information about the memory layout of the array.

C_CONTIGUOUS(C)

The data is in a single, C-style contiguous segment.

F_CONTIGUOUS(F)

The data is in a single, Fortran-style contiguous segment.

OWNDATA(O)

The array owns the memory it uses or borrows it from another object.

WRITEABLE(W)

The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.

ALIGNED(A)

The data and all elements are aligned appropriately for the hardware.

WRITEBACKIFCOPY(X)

This array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.

FNC

F_CONTIGUOUS and not C_CONTIGUOUS.

FORC

F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).

BEHAVED(B)

ALIGNED and WRITEABLE.

CARRAY(CA)

BEHAVED and C_CONTIGUOUS.

FARRAY(FA)

BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.

Notes

The flags object can be accessed dictionary-like (as in a.flags['WRITEABLE']), or by using lowercased attribute names (as in a.flags.writeable). Short flag names are only supported in dictionary access.

Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling ndarray.setflags.

The array flags cannot be set arbitrarily:

  • WRITEBACKIFCOPY can only be set False.

  • ALIGNED can only be set True if the data is truly aligned.

  • WRITEABLE can only be set True if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.

Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.

Even for contiguous arrays a stride for a given dimension arr.strides[dim] may be arbitrary if arr.shape[dim] == 1 or the array has no elements. It does not generally hold that self.strides[-1] == self.itemsize for C-style contiguous arrays or self.strides[0] == self.itemsize for Fortran-style contiguous arrays is true.

flat

A 1-D iterator over the array.

This is a numpy.flatiter instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.

See also

flatten

Return a copy of the array collapsed into one dimension.

flatiter

Examples

>>> x = np.arange(1, 7).reshape(2, 3)
>>> x
array([[1, 2, 3],
       [4, 5, 6]])
>>> x.flat[3]
4
>>> x.T
array([[1, 4],
       [2, 5],
       [3, 6]])
>>> x.T.flat[3]
5
>>> type(x.flat)
<class 'numpy.flatiter'>

An assignment example:

>>> x.flat = 3; x
array([[3, 3, 3],
       [3, 3, 3]])
>>> x.flat[[1,4]] = 1; x
array([[3, 1, 3],
       [3, 1, 3]])
flatten(order='C')

Return a copy of the array collapsed into one dimension.

Parameters:

order ({'C', 'F', 'A', 'K'}, optional) – ‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran- style) order. ‘A’ means to flatten in column-major order if a is Fortran contiguous in memory, row-major order otherwise. ‘K’ means to flatten a in the order the elements occur in memory. The default is ‘C’.

Returns:

y (ndarray) – A copy of the input array, flattened to one dimension.

See also

ravel

Return a flattened array.

flat

A 1-D flat iterator over the array.

Examples

>>> a = np.array([[1,2], [3,4]])
>>> a.flatten()
array([1, 2, 3, 4])
>>> a.flatten('F')
array([1, 3, 2, 4])
free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

getfield(dtype, offset=0)

Returns a field of the given array as a certain type.

A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.

Parameters:

  • dtype (str or dtype) – The data type of the view. The dtype size of the view can not be larger than that of the array itself.

  • offset (int) – Number of bytes to skip before beginning the element view.

Examples

>>> x = np.diag([1.+1.j]*2)
>>> x[1, 1] = 2 + 4.j
>>> x
array([[1.+1.j,  0.+0.j],
       [0.+0.j,  2.+4.j]])
>>> x.getfield(np.float64)
array([[1.,  0.],
       [0.,  2.]])

By choosing an offset of 8 bytes we can select the complex part of the array for our view:

>>> x.getfield(np.float64, offset=8)
array([[1.,  0.],
       [0.,  4.]])
imag

The imaginary part of the array.

Examples

>>> x = np.sqrt([1+0j, 0+1j])
>>> x.imag
array([ 0.        ,  0.70710678])
>>> x.imag.dtype
dtype('float64')
is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

item(*args)

Copy an element of an array to a standard Python scalar and return it.

Parameters:

*args (Arguments (variable number and type)) –

  • none: in this case, the method only works for arrays with one element (a.size == 1), which element is copied into a standard Python scalar object and returned.

  • int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.

  • tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.

Returns:

z (Standard Python scalar object) – A copy of the specified element of the array as a suitable Python scalar

Notes

When the data type of a is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.

item is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.

Examples

>>> np.random.seed(123)
>>> x = np.random.randint(9, size=(3, 3))
>>> x
array([[2, 2, 6],
       [1, 3, 6],
       [1, 0, 1]])
>>> x.item(3)
1
>>> x.item(7)
0
>>> x.item((0, 1))
2
>>> x.item((2, 2))
1
itemset(*args)

Insert scalar into an array (scalar is cast to array’s dtype, if possible)

There must be at least 1 argument, and define the last argument as item. Then, a.itemset(*args) is equivalent to but faster than a[args] = item. The item should be a scalar value and args must select a single item in the array a.

Parameters:

*args (Arguments) – If one argument: a scalar, only used in case a is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.

Notes

Compared to indexing syntax, itemset provides some speed increase for placing a scalar into a particular location in an ndarray, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using itemset (and item) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration.

Examples

>>> np.random.seed(123)
>>> x = np.random.randint(9, size=(3, 3))
>>> x
array([[2, 2, 6],
       [1, 3, 6],
       [1, 0, 1]])
>>> x.itemset(4, 0)
>>> x.itemset((2, 2), 9)
>>> x
array([[2, 2, 6],
       [1, 0, 6],
       [1, 0, 9]])
itemsize

Length of one array element in bytes.

Examples

>>> x = np.array([1,2,3], dtype=np.float64)
>>> x.itemsize
8
>>> x = np.array([1,2,3], dtype=np.complex128)
>>> x.itemsize
16
label: str = None
max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)

Return the maximum along a given axis.

Refer to numpy.amax for full documentation.

See also

numpy.amax

equivalent function

mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)

Returns the average of the array elements along given axis.

Refer to numpy.mean for full documentation.

See also

numpy.mean

equivalent function

min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)

Return the minimum along a given axis.

Refer to numpy.amin for full documentation.

See also

numpy.amin

equivalent function

nbytes

Total bytes consumed by the elements of the array.

Notes

Does not include memory consumed by non-element attributes of the array object.

See also

sys.getsizeof

Memory consumed by the object itself without parents in case view. This does include memory consumed by non-element attributes.

Examples

>>> x = np.zeros((3,5,2), dtype=np.complex128)
>>> x.nbytes
480
>>> np.prod(x.shape) * x.itemsize
480
ndim

Number of array dimensions.

Examples

>>> x = np.array([1, 2, 3])
>>> x.ndim
1
>>> y = np.zeros((2, 3, 4))
>>> y.ndim
3
newbyteorder(new_order='S', /)

Return the array with the same data viewed with a different byte order.

Equivalent to:

arr.view(arr.dtype.newbytorder(new_order))

Changes are also made in all fields and sub-arrays of the array data type.

Parameters:

new_order (string, optional) –

Byte order to force; a value from the byte order specifications below. new_order codes can be any of:

  • ’S’ - swap dtype from current to opposite endian

  • {‘<’, ‘little’} - little endian

  • {‘>’, ‘big’} - big endian

  • {‘=’, ‘native’} - native order, equivalent to sys.byteorder

  • {‘|’, ‘I’} - ignore (no change to byte order)

The default value (‘S’) results in swapping the current byte order.

Returns:

new_arr (array) – New array object with the dtype reflecting given change to the byte order.

nonzero()

Return the indices of the elements that are non-zero.

Refer to numpy.nonzero for full documentation.

See also

numpy.nonzero

equivalent function

partition(kth, axis=-1, kind='introselect', order=None)

Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.

Added in version 1.8.0.

Parameters:

  • kth (int or sequence of ints) –

    Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.

    Deprecated since version 1.22.0: Passing booleans as index is deprecated.

  • axis (int, optional) – Axis along which to sort. Default is -1, which means sort along the last axis.

  • kind ({'introselect'}, optional) – Selection algorithm. Default is ‘introselect’.

  • order (str or list of str, optional) – When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.

See also

numpy.partition

Return a partitioned copy of an array.

argpartition

Indirect partition.

sort

Full sort.

Notes

See np.partition for notes on the different algorithms.

Examples

>>> a = np.array([3, 4, 2, 1])
>>> a.partition(3)
>>> a
array([2, 1, 3, 4])

>>> a.partition((1, 3))
>>> a
array([1, 2, 3, 4])
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)

Return the product of the array elements over the given axis

Refer to numpy.prod for full documentation.

See also

numpy.prod

equivalent function

ptp(axis=None, out=None, keepdims=False)

Peak to peak (maximum - minimum) value along a given axis.

Refer to numpy.ptp for full documentation.

See also

numpy.ptp

equivalent function

put(indices, values, mode='raise')

Set a.flat[n] = values[n] for all n in indices.

Refer to numpy.put for full documentation.

See also

numpy.put

equivalent function

ravel([order])

Return a flattened array.

Refer to numpy.ravel for full documentation.

See also

numpy.ravel

equivalent function

ndarray.flat

a flat iterator on the array.

real

The real part of the array.

Examples

>>> x = np.sqrt([1+0j, 0+1j])
>>> x.real
array([ 1.        ,  0.70710678])
>>> x.real.dtype
dtype('float64')

See also

numpy.real

equivalent function

repeat(repeats, axis=None)

Repeat elements of an array.

Refer to numpy.repeat for full documentation.

See also

numpy.repeat

equivalent function

reshape(shape, order='C')

Returns an array containing the same data with a new shape.

Refer to numpy.reshape for full documentation.

See also

numpy.reshape

equivalent function

Notes

Unlike the free function numpy.reshape, this method on ndarray allows the elements of the shape parameter to be passed in as separate arguments. For example, a.reshape(10, 11) is equivalent to a.reshape((10, 11)).

resize(new_shape, refcheck=True)

Change shape and size of array in-place.

Parameters:

  • new_shape (tuple of ints, or n ints) – Shape of resized array.

  • refcheck (bool, optional) – If False, reference count will not be checked. Default is True.

Returns:

None

Raises:

  • ValueError – If a does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.

  • SystemError – If the order keyword argument is specified. This behaviour is a bug in NumPy.

See also

resize

Return a new array with the specified shape.

Notes

This reallocates space for the data area if necessary.

Only contiguous arrays (data elements consecutive in memory) can be resized.

The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set refcheck to False.

Examples

Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:

>>> a = np.array([[0, 1], [2, 3]], order='C')
>>> a.resize((2, 1))
>>> a
array([[0],
       [1]])

>>> a = np.array([[0, 1], [2, 3]], order='F')
>>> a.resize((2, 1))
>>> a
array([[0],
       [2]])

Enlarging an array: as above, but missing entries are filled with zeros:

>>> b = np.array([[0, 1], [2, 3]])
>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
>>> b
array([[0, 1, 2],
       [3, 0, 0]])

Referencing an array prevents resizing…

>>> c = a
>>> a.resize((1, 1))
Traceback (most recent call last):
...
ValueError: cannot resize an array that references or is referenced ...

Unless refcheck is False:

>>> a.resize((1, 1), refcheck=False)
>>> a
array([[0]])
>>> c
array([[0]])
round(decimals=0, out=None)

Return a with each element rounded to the given number of decimals.

Refer to numpy.around for full documentation.

See also

numpy.around

equivalent function

searchsorted(v, side='left', sorter=None)

Find indices where elements of v should be inserted in a to maintain order.

For full documentation, see numpy.searchsorted

See also

numpy.searchsorted

equivalent function

setfield(val, dtype, offset=0)

Put a value into a specified place in a field defined by a data-type.

Place val into a’s field defined by dtype and beginning offset bytes into the field.

Parameters:

  • val (object) – Value to be placed in field.

  • dtype (dtype object) – Data-type of the field in which to place val.

  • offset (int, optional) – The number of bytes into the field at which to place val.

Returns:

None

See also

getfield

Examples

>>> x = np.eye(3)
>>> x.getfield(np.float64)
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])
>>> x.setfield(3, np.int32)
>>> x.getfield(np.int32)
array([[3, 3, 3],
       [3, 3, 3],
       [3, 3, 3]], dtype=int32)
>>> x
array([[1.0e+000, 1.5e-323, 1.5e-323],
       [1.5e-323, 1.0e+000, 1.5e-323],
       [1.5e-323, 1.5e-323, 1.0e+000]])
>>> x.setfield(np.eye(3), np.int32)
>>> x
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])
setflags(write=None, align=None, uic=None)

Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.

These Boolean-valued flags affect how numpy interprets the memory area used by a (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)

Parameters:

  • write (bool, optional) – Describes whether or not a can be written to.

  • align (bool, optional) – Describes whether or not a is aligned properly for its type.

  • uic (bool, optional) – Describes whether or not a is a copy of another “base” array.

Notes

Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.

WRITEABLE (W) the data area can be written to;

ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);

WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.

All flags can be accessed using the single (upper case) letter as well as the full name.

Examples

>>> y = np.array([[3, 1, 7],
...               [2, 0, 0],
...               [8, 5, 9]])
>>> y
array([[3, 1, 7],
       [2, 0, 0],
       [8, 5, 9]])
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
>>> y.setflags(write=0, align=0)
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : False
  ALIGNED : False
  WRITEBACKIFCOPY : False
>>> y.setflags(uic=1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: cannot set WRITEBACKIFCOPY flag to True
shape

Tuple of array dimensions.

The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.

Warning

Setting arr.shape is discouraged and may be deprecated in the future. Using ndarray.reshape is the preferred approach.

Examples

>>> x = np.array([1, 2, 3, 4])
>>> x.shape
(4,)
>>> y = np.zeros((2, 3, 4))
>>> y.shape
(2, 3, 4)
>>> y.shape = (3, 8)
>>> y
array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
>>> y.shape = (3, 6)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: total size of new array must be unchanged
>>> np.zeros((4,2))[::2].shape = (-1,)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: Incompatible shape for in-place modification. Use
`.reshape()` to make a copy with the desired shape.

See also

numpy.shape

Equivalent getter function.

numpy.reshape

Function similar to setting shape.

ndarray.reshape

Method similar to setting shape.

size

Number of elements in the array.

Equal to np.prod(a.shape), i.e., the product of the array’s dimensions.

Notes

a.size returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested np.prod(a.shape), which returns an instance of np.int_), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.

Examples

>>> x = np.zeros((3, 5, 2), dtype=np.complex128)
>>> x.size
30
>>> np.prod(x.shape)
30
sort(axis=-1, kind=None, order=None)

Sort an array in-place. Refer to numpy.sort for full documentation.

Parameters:

  • axis (int, optional) – Axis along which to sort. Default is -1, which means sort along the last axis.

  • kind ({'quicksort', 'mergesort', 'heapsort', 'stable'}, optional) –

    Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.

    Changed in version 1.15.0: The ‘stable’ option was added.

  • order (str or list of str, optional) – When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.

See also

numpy.sort

Return a sorted copy of an array.

numpy.argsort

Indirect sort.

numpy.lexsort

Indirect stable sort on multiple keys.

numpy.searchsorted

Find elements in sorted array.

numpy.partition

Partial sort.

Notes

See numpy.sort for notes on the different sorting algorithms.

Examples

>>> a = np.array([[1,4], [3,1]])
>>> a.sort(axis=1)
>>> a
array([[1, 4],
       [1, 3]])
>>> a.sort(axis=0)
>>> a
array([[1, 3],
       [1, 4]])

Use the order keyword to specify a field to use when sorting a structured array:

>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
>>> a.sort(order='y')
>>> a
array([(b'c', 1), (b'a', 2)],
      dtype=[('x', 'S1'), ('y', '<i8')])
squeeze(axis=None)

Remove axes of length one from a.

Refer to numpy.squeeze for full documentation.

See also

numpy.squeeze

equivalent function

std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)

Returns the standard deviation of the array elements along given axis.

Refer to numpy.std for full documentation.

See also

numpy.std

equivalent function

strides

Tuple of bytes to step in each dimension when traversing an array.

The byte offset of element (i[0], i[1], ..., i[n]) in an array a is:

offset = sum(np.array(i) * a.strides)

A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.

Warning

Setting arr.strides is discouraged and may be deprecated in the future. numpy.lib.stride_tricks.as_strided should be preferred to create a new view of the same data in a safer way.

Notes

Imagine an array of 32-bit integers (each 4 bytes):

x = np.array([[0, 1, 2, 3, 4],
              [5, 6, 7, 8, 9]], dtype=np.int32)

This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array x will be (20, 4).

See also

numpy.lib.stride_tricks.as_strided

Examples

>>> y = np.reshape(np.arange(2*3*4), (2,3,4))
>>> y
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],
       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])
>>> y.strides
(48, 16, 4)
>>> y[1,1,1]
17
>>> offset=sum(y.strides * np.array((1,1,1)))
>>> offset/y.itemsize
17

>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
>>> x.strides
(32, 4, 224, 1344)
>>> i = np.array([3,5,2,2])
>>> offset = sum(i * x.strides)
>>> x[3,5,2,2]
813
>>> offset / x.itemsize
813
sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)

Return the sum of the array elements over the given axis.

Refer to numpy.sum for full documentation.

See also

numpy.sum

equivalent function

swapaxes(axis1, axis2)

Return a view of the array with axis1 and axis2 interchanged.

Refer to numpy.swapaxes for full documentation.

See also

numpy.swapaxes

equivalent function

take(indices, axis=None, out=None, mode='raise')

Return an array formed from the elements of a at the given indices.

Refer to numpy.take for full documentation.

See also

numpy.take

equivalent function

tobytes(order='C')

Construct Python bytes containing the raw data bytes in the array.

Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the order parameter.

Added in version 1.9.0.

Parameters:

order ({'C', 'F', 'A'}, optional) – Controls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for Any) means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.

Returns:

s (bytes) – Python bytes exhibiting a copy of a’s raw data.

See also

frombuffer

Inverse of this operation, construct a 1-dimensional array from Python bytes.

Examples

>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
>>> x.tobytes()
b'\x00\x00\x01\x00\x02\x00\x03\x00'
>>> x.tobytes('C') == x.tobytes()
True
>>> x.tobytes('F')
b'\x00\x00\x02\x00\x01\x00\x03\x00'
tofile(fid, sep='', format='%s')

Write array to a file as text or binary (default).

Data is always written in ‘C’ order, independent of the order of a. The data produced by this method can be recovered using the function fromfile().

Parameters:

  • fid (file or str or Path) –

    An open file object, or a string containing a filename.

    Changed in version 1.17.0: pathlib.Path objects are now accepted.

  • sep (str) – Separator between array items for text output. If “” (empty), a binary file is written, equivalent to file.write(a.tobytes()).

  • format (str) – Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.

Notes

This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.

When fid is a file object, array contents are directly written to the file, bypassing the file object’s write method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support fileno() (e.g., BytesIO).

tolist()

Return the array as an a.ndim-levels deep nested list of Python scalars.

Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the ~numpy.ndarray.item function.

If a.ndim is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.

Parameters:

none

Returns:

y (object, or list of object, or list of list of object, or …) – The possibly nested list of array elements.

Notes

The array may be recreated via a = np.array(a.tolist()), although this may sometimes lose precision.

Examples

For a 1D array, a.tolist() is almost the same as list(a), except that tolist changes numpy scalars to Python scalars:

>>> a = np.uint32([1, 2])
>>> a_list = list(a)
>>> a_list
[1, 2]
>>> type(a_list[0])
<class 'numpy.uint32'>
>>> a_tolist = a.tolist()
>>> a_tolist
[1, 2]
>>> type(a_tolist[0])
<class 'int'>

Additionally, for a 2D array, tolist applies recursively:

>>> a = np.array([[1, 2], [3, 4]])
>>> list(a)
[array([1, 2]), array([3, 4])]
>>> a.tolist()
[[1, 2], [3, 4]]

The base case for this recursion is a 0D array:

>>> a = np.array(1)
>>> list(a)
Traceback (most recent call last):
  ...
TypeError: iteration over a 0-d array
>>> a.tolist()
1
tostring(order='C')

A compatibility alias for tobytes, with exactly the same behavior.

Despite its name, it returns bytes not strs.

Deprecated since version 1.19.0.

trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)

Return the sum along diagonals of the array.

Refer to numpy.trace for full documentation.

See also

numpy.trace

equivalent function

transpose(*axes)

Returns a view of the array with axes transposed.

Refer to numpy.transpose for full documentation.

Parameters:

axes (None, tuple of ints, or n ints) –

  • None or no argument: reverses the order of the axes.

  • tuple of ints: i in the j-th place in the tuple means that the array’s i-th axis becomes the transposed array’s j-th axis.

  • n ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form).

Returns:

p (ndarray) – View of the array with its axes suitably permuted.

See also

transpose

Equivalent function.

ndarray.T

Array property returning the array transposed.

ndarray.reshape

Give a new shape to an array without changing its data.

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.transpose()
array([[1, 3],
       [2, 4]])
>>> a.transpose((1, 0))
array([[1, 3],
       [2, 4]])
>>> a.transpose(1, 0)
array([[1, 3],
       [2, 4]])

>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> a.transpose()
array([1, 2, 3, 4])
var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)

Returns the variance of the array elements, along given axis.

Refer to numpy.var for full documentation.

See also

numpy.var

equivalent function

view([dtype][, type])

New view of array with the same data.

Note

Passing None for dtype is different from omitting the parameter, since the former invokes dtype(None) which is an alias for dtype('float_').

Parameters:

  • dtype (data-type or ndarray sub-class, optional) – Data-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as a. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the type parameter).

  • type (Python type, optional) – Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.

Notes

a.view() is used two different ways:

a.view(some_dtype) or a.view(dtype=some_dtype) constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.

a.view(ndarray_subclass) or a.view(type=ndarray_subclass) just returns an instance of ndarray_subclass that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.

For a.view(some_dtype), if some_dtype has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of a must be contiguous. This axis will be resized in the result.

Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.

Examples

>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])

Viewing array data using a different type and dtype:

>>> y = x.view(dtype=np.int16, type=np.matrix)
>>> y
matrix([[513]], dtype=int16)
>>> print(type(y))
<class 'numpy.matrix'>

Creating a view on a structured array so it can be used in calculations

>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
>>> xv = x.view(dtype=np.int8).reshape(-1,2)
>>> xv
array([[1, 2],
       [3, 4]], dtype=int8)
>>> xv.mean(0)
array([2.,  3.])

Making changes to the view changes the underlying array

>>> xv[0,1] = 20
>>> x
array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])

Using a view to convert an array to a recarray:

>>> z = x.view(np.recarray)
>>> z.a
array([1, 3], dtype=int8)

Views share data:

>>> x[0] = (9, 10)
>>> z[0]
(9, 10)

Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:

>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
>>> y = x[:, ::2]
>>> y
array([[1, 3],
       [4, 6]], dtype=int16)
>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
Traceback (most recent call last):
    ...
ValueError: To change to a dtype of a different size, the last axis must be contiguous
>>> z = y.copy()
>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
array([[(1, 3)],
       [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])

However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:

>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
>>> x.transpose(1, 0, 2).view(np.int16)
array([[[ 256,  770],
        [3340, 3854]],

       [[1284, 1798],
        [4368, 4882]],

       [[2312, 2826],
        [5396, 5910]]], dtype=int16)
walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableNode

Bases: Evaluatable[EvaluatedType]

Base class representing a computable node in an expression tree.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableSingleChild

Bases: ComputableNode[EvaluatedType]

Computable class which has a single child.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ComputableTuple(*items: Any)

Bases: tuple, ComputableNode[Tuple]

Class representing a tuple of items of any types in the computable expression tree.

Parameters:

*items – One or more items, which can be of any type.

Example

>>> from inquanto.computables.primitive import ComputableInt
>>> k_tuple = ComputableTuple(ComputableInt(1), ComputableInt(2), 3, "foo")
>>> k_tuple
(ComputableInt(value=1), ComputableInt(value=2), 3, 'foo')
>>> len(k_tuple)
4
>>> k_tuple.evaluate()
(1, 2, 3, 'foo')
children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator

evaluate(evaluator=None)

Evaluates each item in the tuple and returns the computed results as a tuple.

If an item is a computable, its evaluate() method is called. Otherwise, the item itself is returned.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Any]], default: None) – Callable passed to each item’s evaluate() method.

Returns:

Union[ComputableTuple, Tuple] – The computed results of the items.

class Evaluatable

Bases: Generic[EvaluatedType]

Base class for classes that have evaluate() methods.

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(EvaluatableType, bound= Evaluatable), TypeVar(EvaluatedType)] – The computed result.

inquanto.computables.composite

Submodule for composite quantum computable expressions. Composed of atomic computables.

class CommutatorComputable(state, operator_left, operator_right)

Bases: ComputableSingleChild[complex]

Computable expression to calculate the expectation value of commutator between two qubit operators.

Represents the expression \(\langle \Psi | [A, B] | \Psi\rangle\).

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ExpectationValueSumComputable(states, kernels)

Bases: ComputableSingleChild[float]

Computable expression to calculate the sum of expectation values with different states and hermitian kernels.

Represents the expression \(\sum_i \langle \psi_i | A | \psi_i \rangle\) or \(\sum_i \langle \psi_i | A_i | \psi_i \rangle\).

Parameters:
Raises:

ValueError – If a list of kernels is provided which is not the same length as states.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class HoleGFComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())

Bases: ComputableSingleChild[Expr]

Computable expression for the Many-body hole Green’s function.

Internally it measures the moments to compute the Lanczos coefficients, and it will be used to evaluate the Green’s function matrix elements.

Parameters:

  • state (GeneralAnsatz) – Initial ansatz state.

  • kernel (QubitOperator) – Hermitian operator kernel.

  • krylov (int) – Dimension of the Krylov space.

  • left (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the left.

  • right (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of the left.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Expr – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class KrylovSubspace(moments)

Bases: object

Helper class for Lanczos coefficients.

Calculates \(\alpha_n\) and \(\beta_n\) coefficients for the Krylov-space from a list of moments. If the number of moments is \(2*n-1\) then the Krylov-space has a dimension \(n\).

Parameters:

moments (Union[List[float], List[Expr]]) – List of moments as [<>, <H>, <H^2>, ..., <H^(2*n-1)>].

alpha_f(n)

Recursively computes n-th alpha Lanczos coefficient.

Parameters:

n (int) – The n-th Lanczos coefficient.

Returns:

float – The value of alpha.

beta_f(n)

Recursively computes n-th beta Lanczos coefficient.

Parameters:

n (int) – The n-th Lanczos coefficient.

Returns:

float – The value of beta.

construct_symbolic_recursive_gf(z=Symbol('z'), factor=1.0, shift=0.0, tolerance=1e-8)

Generate an expression for the Green’s function with the recursive formulae.

Parameters:

  • z (Union[float, Expr], default: Symbol("z")) – Symbol z is the complex energy.

  • factor (float, default: 1.0) – This is +1 or -1, for particle or hole, respectively.

  • shift (Union[float, Expr], default: 0.0) – The ground energy shift.

  • tolerance (float, default: 1e-8) – Stop the recursion if bn is smaller than the tolerance.

Returns:

Union[float, complex, Expr] – Symbolic expression for G(z) approximation.

construct_symbolic_recursive_gf_h(z=Symbol('z'), e0=Symbol('e0'), eta=Symbol('eta'))

Expression for the hole Green’s function with the recursive formulae.

Note: Equivalent to construct_symbolic_recursive_gf(z, -1, e0 + I * eta).

Parameters:

  • z (Expr, default: Symbol("z")) – Symbol z is the complex energy.

  • e0 (Expr, default: Symbol("e0")) – Ground state energy.

  • eta (Symbol, default: Symbol("eta")) – Magnitude of the small imaginary shift.

Returns:

Union[float, complex, Expr] – Symbolic expression.

construct_symbolic_recursive_gf_p(z=Symbol('z'), e0=Symbol('e0'), eta=Symbol('eta'))

Expression for the particle Green’s function with the recursive formulae.

Note: Equivalent to construct_symbolic_recursive_gf(z, +1, e0 + I * eta).

Parameters:

  • z (Expr, default: Symbol("z")) – Symbol z is the complex energy.

  • e0 (Expr, default: Symbol("e0")) – Ground state energy.

  • eta (Symbol, default: Symbol("eta")) – Magnitude of the small imaginary shift.

Returns:

Union[float, complex, Expr] – Symbolic expression.

construct_symbolic_recursive_lanczos_gf00(z=Symbol('z'))

Expression for the Greens function with the recursive formulae.

Note: Equivalent to construct_symbolic_recursive_gf(z, +1, 0).

Parameters:

z (Expr, default: Symbol("z")) – Symbol z is the complex energy.

Returns:

Union[float, complex, Expr] – Symbolic expression.

construct_tridiagonal_representation()

Constructs the tridiagonal representation of the Hamiltonian.

Returns:

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]] – Tridiagonalized matrix of the Hamiltonian in the Krylov basis.

eigenvalues()

Eigenvalues of the Lanczos matrix.

Returns:

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]] – Array of eigenvalues.

factors()

Calculates the Lanczos coefficients.

Returns:

Tuple[List[float], List[float]] – A tuple of lists, the first list has n alpha values, the second list has n-1 beta values.

lowest_eigenvalue()

The lowest eigenvalues of the Lanczos matrix.

Returns:

float – The lowest eigenvalue.

moments()

Moments internally stored.

Return type:

List[Union[float, Expr]]

class KrylovSubspaceComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())

Bases: ComputableSingleChild[KrylovSubspace]

Computable expression for KrylovSubspace moments.

Based on arXiv:2009.13140 <https://arxiv.org/pdf/2009.13140.pdf>.

Indirectly measures the moments to compute the Lanczos coefficients \(\alpha_n\) and \(\beta_n\) of the Krylov-space.

More precisely, internally it will measure \(\langle\Psi(\theta) | L * H^n * R| \Psi(\theta)\rangle\) where H is a hermitian operator, \(L\), \(R = L^{\dagger}\) are left and right operators, usually identities.

Parameters:

  • state (GeneralAnsatz) – Initial ansatz state.

  • kernel (QubitOperator) – Hermitian operator kernel.

  • krylov (int) – Dimension of the Krylov space.

  • left (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the left.

  • right (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of the left.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

KrylovSubspace – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class LanczosCoefficientsComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())

Bases: ComputableSingleChild[Tuple[List[float], List[float]]]

Computable expression for the Lanczos coefficients.

Internally it measures the moments to compute the Lanczos coefficients \(\alpha_n\) and \(\beta_n\) of the Krylov-space.

Parameters:

  • state (GeneralAnsatz) – Initial ansatz state.

  • kernel (QubitOperator) – Hermitian operator kernel.

  • krylov (int) – Dimension of the Krylov space.

  • left (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the left.

  • right (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of the left.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Tuple[List[float], List[float]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class LanczosMatrixComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())

Bases: ComputableSingleChild[ndarray[Any, dtype[_ScalarType_co]]]

Computable expression for the tridiagonal Lanczos matrix.

Internally it measures the moments to compute the tridiagonal Lanczos matrix with coefficients \(\alpha_n\) and \(\beta_n\) of the Krylov-space.

Parameters:

  • state (GeneralAnsatz) – Initial ansatz state.

  • kernel (QubitOperator) – Hermitian operator kernel.

  • krylov (int) – Dimension of the Krylov space.

  • left (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the left.

  • right (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of the left.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ManyBodyGFComputable(fermion_space, ground_state, hamiltonian, krylov, encoding=QubitMappingJordanWigner(), ground_state_energy=None, eta=0)

Bases: ComputableSingleChild[MutableDenseMatrix]

Computable expression for the 1-particle Many-Body Green’s function matrix, in a basis of spin orbitals.

Parameters:

  • fermion_space (FermionSpace) – Fermion occupation space described by this Green’s function.

  • ground_state (GeneralAnsatz) – Ground state.

  • hamiltonian (Union[QubitOperator, FermionOperator]) – Hamiltonian of the system.

  • krylov (int) – Dimension of the Krylov space.

  • encoding (QubitMapping, default: QubitMappingJordanWigner()) – Fermion to qubit mapping.

  • ground_state_energy (Optional[float], default: None) – Ground state energy.

  • eta (Union[Symbol, float], default: 0) – Infinitesimal number for the many-body Green’s function.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

default_evaluate_as_function(parameters=None)

Evaluates to a function with the default protocol.

Evaluates the Green’s function matrix with the default protocol and simulator and constructs a function from complex energy to a numpy matrix.

Returns:

Callable[[Union[float, complex]], ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – A function \(G(z)\) that returns a numpy matrix.

Parameters:

parameters (Union[SymbolDict, Dict], default: None)

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

MutableDenseMatrix – The computed result.

evaluate_as_function(evaluator=None)

Evaluates to a function.

Evaluates the GF matrix and constructs a function from complex energy to a numpy matrix.

Returns:

Callable[[Union[float, complex]], ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – A function \(G(z)\) that returns a numpy matrix.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None)

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class NonOrthogonalMatricesComputable(hermitian_operator, states)

Bases: ComputableNode

Computable expression representing NO (Non Orthogonal) matrices.

Measure matrix elements of a matrix \(H\) and overlap matrix \(S\) in the generalised eigenvalue equation \(HC = eSC\). The \(H\) matrix is the matrix representation of a Hermitian operator, typically the Hamiltonian, in the subspace spanned by a list of states, and \(S\) is the overlap matrix of the states.

Both, \(H\) and \(S\) matrices are represented with OverlapMatrixComputable internally.

Based on arxiv.org/abs/2205.09039.

Parameters:

  • hermitian_operator (QubitOperator) – A Hermitian operator, typically a Hamiltonian, to be expanded in the subspace.

  • states (List[GeneralAnsatz]) – Ansatz states used to span the subspace.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[NonOrthogonalMatricesComputable, Tuple[ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]], ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class OverlapMatrixComputable(states, kernel=QubitOperator.identity())

Bases: ComputableNode

Computable expression representing an overlap matrix.

The general overlap matrix defined as \(S_{ij} = \langle\Psi_i|\hat{O}|\Psi_j\rangle\) where \(\hat{O}\) kernel is a Hermitian qubit operator and \(|\Psi_i\rangle\) are normalised states as ansatzes.

The diagonal elements of the overlap matrix are represented with ExpectationValue computables if the kernel is not identity, while the off-diagonal elements are represented with Overlap computables. Since the overlap matrix is a Hermitian matrix, the lower triangular part is excluded from any subsequent measurements or simulation workflow and on evaluation it is computed from the upper triangular part. If the kernel is identity, the diagonal elements are set to 1 and the expectation values are not included into any measurements or simulation workflow.

Parameters:

  • states (List[GeneralAnsatz]) – Ansatz states used to span the subspace.

  • kernel (QubitOperator, default: QubitOperator.identity()) – An optional Hermitian operator, by default it is identity.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[OverlapMatrixComputable, ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class PDM1234RealComputable(space, ansatz, encoding, symmetry_operators, cas_elec, cas_orbs, cu4=True, taperer=None)

Bases: ComputableSingleChild[Tuple[ndarray[Any, dtype[_ScalarType_co]], …]]

Computable expressions for 1,2,3-PDMs of a given state, defined by ansatz and parameters.

Represents the Pre-Density Matrix (PDM) according to doi.org/10.1063/5.0051211.

Parameters:

  • space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

  • symmetry_operators (List[SymmetryOperatorPauli]) – Z2 symmetries of the Hamiltonian.

  • cas_elec (int) – Number of active electrons.

  • cas_orbs (int) – Number of active orbitals.

  • cu4 (bool, default: True) – If True (default), the 4-PDM is estimated via the cumulant expansion approximation, otherwise it is measured.

  • taperer (Optional[TapererZ2], default: None) – TapererZ2 initialized with the Hamiltonian, or None if tapering is not used.

Note

1,2,3,4-PDMs are returned as a list of arrays, in PySCF-style ordering (<p^r^sq>)

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

  • evaluator – A callable evaluator that is called on the instance.

  • args (Any)

  • kwargs (Any)

Returns:

Tuple[ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]], ...] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class ParticleGFComputable(state, kernel, krylov, left=QubitOperator.identity(), right=QubitOperator.identity())

Bases: ComputableSingleChild[Expr]

Computable expression for the Many-body particle Green’s function.

Internally it measures the moments to compute the Lanczos coefficients, and it will be used to evaluate the Green’s function matrix elements.

Parameters:

  • state (GeneralAnsatz) – Initial ansatz state.

  • kernel (QubitOperator) – Hermitian operator kernel.

  • krylov (int) – Dimension of the Krylov space.

  • left (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the left.

  • right (QubitOperator, default: QubitOperator.identity()) – Optional operator to transform the moments from the right, currently assumed to be the hermitian conjugate of the left.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Expr – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class QCM4Computable(state, kernel)

Bases: ComputableSingleChild[KrylovSubspace]

Computable expression for infimum approximation quantum computed moments up to order of 4.

Based on arXiv:2311.02533 <https://arxiv.org/pdf/2311.02533>.

Parameters:
__init__(state, kernel)

Quantum computed moment computable to approximate the lowest eigenvalue of the kernel.

Parameters:
add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class QSEMatricesComputable(state, hermitian_operator, expansion_operators)

Bases: ComputableNode

Computable expression representing QSE (quantum subspace expansion) matrices.

Measure matrix elements of a matrix \(H\) and overlap matrix \(S\) in the generalised eigenvalue equation \(HC = eSC\). The \(H\) matrix is the matrix representation of a Hermitian operator, typically the Hamiltonian, in the subspace spanned by the excitation operators, and \(S\) is the overlap matrix of the subspace generating states. QSE aims to obtain a description of low-lying excited states described as an expansion of excitation operators acting on the effective ground-state obtained from a variational calculation.

Based on arXiv:1603.05681.

Parameters:

  • state (GeneralAnsatz) – Ansatz used to represent the ground state, it is used as a reference state for the excitations to generate the subspace.

  • hermitian_operator (QubitOperator) – A Hermitian operator, typically a Hamiltonian, to be expanded in the subspace.

  • expansion_operators (List[QubitOperator]) – A List of excitation operators spanning the subspace.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator – A callable evaluator that is called on the instance.

Returns:

Tuple[ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]], ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class RDM1234RealComputable(space, ansatz, encoding, symmetry_operators, cas_elec, cas_orbs, cu4=True, taperer=None)

Bases: ComputableSingleChild[List[ndarray[Any, dtype[_ScalarType_co]]]]

Computable expression for 1,2,3-RDMs of a given state, defined by ansatz and parameters.

Parameters:

  • space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

  • symmetry_operators (List[SymmetryOperatorPauli]) – Z2 symmetries of the Hamiltonian.

  • cas_elec (int) – Number of active electrons.

  • cas_orbs (int) – Number of active orbitals.

  • cu4 (bool, default: True) – If True (default), the 4-RDM is estimated via the cumulant expansion approximation, otherwise it is measured.

  • taperer (Optional[TapererZ2], default: None) – TapererZ2 initialized with the Hamiltonian, or None if tapering is not used.

Note

1,2,3,4-RDMs are returned as a list of arrays, in PySCF-style ordering (<p^r^sq>)

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

  • evaluator – A callable evaluator that is called on the instance.

  • args (Any)

  • kwargs (Any)

Returns:

List[ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class RestrictedOneBodyRDMComputable(fermion_space, ansatz, encoding)

Bases: _BaseCollinearOneBodyRDMComputable

Computable expression for a RestrictedOneBodyRDM.

Parameters:

  • fermion_space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator – A callable evaluator that is called on the instance.

Returns:

RestrictedOneBodyRDM – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class RestrictedOneBodyRDMRealComputable(fermion_space, ansatz, encoding)

Bases: _BaseCollinearOneBodyRDMComputable

Computable expression for the real part of a RestrictedOneBodyRDM.

Parameters:

  • fermion_space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator – A callable evaluator that is called on the instance.

Returns:

RestrictedOneBodyRDM – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class SCEOMMatrixComputable(space, fermion_state, ground_state, mapping, hermitian_operator, expansion_operators, pointgroup=None)

Bases: ComputableSingleChild

Computable Quantum Self Consistent Equation of Motion (SCEOM) matrix.

Implementation based on doi.org/10.1039/D2SC05371C.

Parameters:

  • space (FermionSpace) – Fermion Space object.

  • fermion_state (FermionState) – The inquanto datastructure for a parametric-state, which contains a symbolic circuit and a symbol register.

  • ground_state (GeneralAnsatz) – Ground state as ansatz to be used as starting state for the SCEOM matrix.

  • mapping (QubitMapping) – Qubit mappings to be used.

  • hermitian_operator (QubitOperator) – A dictionary mapping QubitPauliStrings to coefficients. A QubitPauliString maps UnitIDs of qubits to Paulis.

  • expansion_operators (Iterable[QubitOperator]) – A list of expansion operators to build a subspace around a reference-state.

  • pointgroup (str, default: None) – Point Group symmetry used for reducing matrix elements to be calculated.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

check_energies(eigvs)

Returns a computable list of the energies of the SCEOM eigenstates.

Note

This should be the same as the eigenvalues of the SCEOM matrix.

Parameters:

eigvs (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – Eigenvector of the SCEOM matrix.

Returns:

ComputableList – Computable list of expectation values of the Hamiltonian.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[SCEOMMatrixComputable, ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

get_overlap_computables(eigvs)

Returns a computable list of overlaps of ground state with the SCEOM eigenstates.

Parameters:

eigvs (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – Eigenvector of the SCEOM matrix.

Returns:

ComputableList – Computable list of overlaps.

get_s2_computables(eigvs)

Returns a computable list of expectation values of S^2 with SCEOM eigenstates.

Parameters:

eigvs (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – Eigenvector of the SCEOM matrix.

Returns:

ComputableList – Computable list of expectation values.

get_sz_computables(eigvs)

Returns a computable list of expectation values of Sz with SCEOM eigenstates.

Parameters:

eigvs (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – Eigenvector of the SCEOM matrix.

Returns:

ComputableList – Computable list of expectation values.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class SpinlessNBodyPDMArrayRealComputable(n, fermion_space, ansatz, encoding, symmetry_operators, taperer=None)

Bases: ComputableSingleChild[ndarray[Any, dtype[_ScalarType_co]]]

Computable expression for spinless, n-body PDM (Pre-Density Matrix).

Calculates a general n-body PDM \(\gamma^{i\dots j}_{m\dots n} = \bra{\Psi_0} \hat{E}^{i}_{n} \hat{E}^{j}_{n}\dots \ket{\Psi_0}\) where \(\hat{E}^{i}_{n}\) is a spin-traced excitation operator, defined as: \(\hat{E}^{p}_{q} = \hat{a}^{\dagger}_{p\uparrow}\hat{a}_{q\uparrow}+ \hat{a}^{\dagger}_{p\downarrow}\hat{a}_{q\downarrow}\). For example, in the four-body case, PDM is:

\(\gamma^{prtv}_{qsuw} = \bra{\Psi_0} \hat{E}^{p}_{q}\hat{E}^{r}_{s}\hat{E}^{t}_{u}\hat{E}^{v}_{w} \ket{\Psi_0}\).

Parameters:

  • n (int) – Order of n-body PDM.

  • fermion_space (FermionSpace) – Fermion occupation space spanned by this PDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

  • symmetry_operators (List[SymmetryOperatorPauli]) – List of Z2 symmetries of the Hamiltonian.

  • taperer (Optional[TapererZ2], default: None) – Optional taperer object.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class SpinlessNBodyRDMArrayRealComputable(n, fermion_space, ansatz, encoding, symmetry_operators, taperer=None, ordering='p^r^sq')

Bases: ComputableSingleChild[ndarray[Any, dtype[_ScalarType_co]]]

Computable expression for spinless, n-body RDM matrices.

Calculates a general n-body RDM \(\Gamma^{i\dots j}_{n\dots m} = \bra{\Psi_0} \hat{E}^{i\dots j}_{n\dots m} \ket{\Psi_0}\) where \(\hat{E}^{i\dots j}_{n\dots m}\) is a spin-traced excitation operator. For example, in the one-body case this is:

\(\hat{E}^{p}_{q} = \hat{a}^{\dagger}_{p\uparrow}\hat{a}_{q\uparrow}+ \hat{a}^{\dagger}_{p\downarrow}\hat{a}_{q\downarrow}\).

And in the two-body case:

\(\hat{E}^{pr}_{qs}= \hat{a}^{\dagger}_{p\uparrow}\hat{a}^{\dagger}_{r\uparrow}\hat{a}_{s\uparrow}\hat{a}_{q\uparrow} +\hat{a}^{\dagger}_{p\uparrow}\hat{a}^{\dagger}_{r\downarrow}\hat{a}_{s\downarrow}\hat{a}_{q\uparrow} +\hat{a}^{\dagger}_{p\downarrow}\hat{a}^{\dagger}_{r\uparrow}\hat{a}_{s\uparrow}\hat{a}_{q\downarrow} +\hat{a}^{\dagger}_{p\downarrow}\hat{a}^{\dagger}_{r\downarrow}\hat{a}_{s\downarrow}\hat{a}_{q\downarrow}\).

Parameters:

  • n (int) – n-body RDM.

  • fermion_space (FermionSpace) – Fermion space where the operators are defined.

  • ansatz (GeneralAnsatz) – Ansatz with respect to which the expectation values are computed.

  • encoding (QubitMapping) – Qubit encoding from fermion space to qubit space.

  • symmetry_operators (List[SymmetryOperatorPauli]) – List of Z2 symmetries of the Hamiltonian.

  • taperer (Optional[TapererZ2], default: None) – Optional taperer object.

  • ordering (str, default: "p^r^sq") – RDM index convention. The default corresponds to PySCF.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(evaluator=None)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator (Optional[Callable[[Evaluatable], Union[Evaluatable, Any]]], default: None) – A callable evaluator that is called on the instance.

Returns:

Union[TypeVar(TQCOne, bound= ComputableSingleChild), TypeVar(EvaluatedType)] – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class UnrestrictedOneBodyRDMComputable(fermion_space, ansatz, encoding)

Bases: _BaseCollinearOneBodyRDMComputable

Computable expression for an UnrestrictedOneBodyRDM.

Parameters:

  • fermion_space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator – A callable evaluator that is called on the instance.

Returns:

UnrestrictedOneBodyRDM – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]

class UnrestrictedOneBodyRDMRealComputable(fermion_space, ansatz, encoding)

Bases: _BaseCollinearOneBodyRDMComputable

Computable expression for the real part of an UnrestrictedOneBodyRDM.

Parameters:

  • fermion_space (FermionSpace) – Fermion occupation space spanned by this RDM.

  • ansatz (GeneralAnsatz) – Ansatz state with respect to which expectation values are computed.

  • encoding (QubitMapping) – Fermion to qubit mapping.

add_label(label, label_children=False)

Assign a label to the current computable.

Overwrites any existing label. Access a computable node’s label with label.

Parameters:

  • label (str) – Label string to be assigned to node. Overwrites any existing label.

  • label_children (bool, default: False) – If True, all child nodes of this computable are labeled with label. If False, children remain unlabeled.

Returns:

ComputableNode – Self.

children()

Generator method that yields the child computable nodes of the current computable node.

Yields:

An iterator over the child computable nodes of the current computable node.

Return type:

Iterator[ComputableNode]

default_evaluate(parameters, protocol=None)

Evaluate the final results immediately for return.

If a protocol is not given it will attempt to use statevector backends from pytket-extensions. First, it will try the AerStateBackend from pytket-qiskit, and then the QulacsBackend from pytket-qulacs.

Parameters:

  • parameters (SymbolDict) – SymbolDict or dict to map symbols to values.

  • protocol (Optional[Any], default: None) – Optional protocol is assumed to be capable of measuring and evaluating the internal quantities to calculate the final value.

Returns:

Union[Evaluatable, Any] – Final value of the evaluatable object.

evaluate(*args, **kwargs)

Evaluate this object using the provided evaluator function.

Parameters:

evaluator – A callable evaluator that is called on the instance.

Returns:

UnrestrictedOneBodyRDM – The computed result.

free_symbols()

Returns the union of free symbols from all children.

Returns:

Set[Symbol] – A set containing the free symbols from all children.

free_symbols_ordered()

Returns the free symbols in increasing lexicographic order as SymbolSet.

Returns:

SymbolSet – Ordered free symbols in object.

is_leaf()

Check if the current computable node is a leaf (i.e., it has no children).

Returns:

bool – True if the computable node is a leaf, False otherwise.

label: str = None
print_tree()

Prints the nodes of the computable expression tree, with an indentation level proportional to their depth.

Return type:

None

walk(depth=0)

Generator method to traverse the computable expression tree in a depth-first manner.

Parameters:

depth (int, default: 0) – The initial depth of the tree. Default is 0.

Yields:

A tuple containing the current computable node and its depth in the tree.

Return type:

Iterator[Tuple[ComputableNode, int]]