How to use InQuanto

InQuanto is a modular Python library with components that fit together to allow bespoke quantum computational chemistry calculations. Whilst InQuanto can be used in a reasonably black-box manner, the user is recommended to have some familiarity with modern computational chemistry and quantum computational chemistry.

In the figure below we show how the key components in InQuanto can be brought together. More in-depth guides on each of these components can be found in this user guide.


Fig. 2 Schematic overview of the InQuanto workflow.

Chemistry Workflows

In InQuanto, algorithms solve quantum computational problems representing chemical systems and quantities of interest. The classes in this module, such as AlgorithmVQE, include quantum and hybrid quantum-classical methods which we may apply to evaluate meaningful chemical quantities, such as ground and excited states. The choice of algorithm may be determined by the problem of interest. See Algorithms.

Algorithms use computables. Computables are expressions representing physical or chemical quantities that one may want to compute with a quantum circuit. A basic example of a computable is the ExpectationValue of a quantum state, such as the total energy of the system as reported by the Hamiltonian. Computables are symbolic, contain the ingredients needed to give the quantity of interest, and their evaluation is performed using protocols. Protocols build and contain the quantum circuits required to evaluate a computable, as well as instructions for measuring and interpreting quantum measurements. See Computables and Protocols for more details.

These algorithms also use pytket backends to drive the quantum computation, and may also need classical functions or data, such as minimizers or a set of initial parameters to aid solution.


InQuanto’s main focus is solving the electronic structure problem of molecules within the Born-Oppenheimer (frozen nuclei) approximation. This is often described using second quantization, such that the Hamiltonian is:

(1)\[\hat{H} = \sum_{i,j=0}^N {h_{ij} a^{\dagger}_{i} a_j} + \frac{1}{2}\sum_{i,j,k,l = 0}^N {h_{ijkl} a^\dagger_i a^\dagger_k a_l a_j}\]

where \(a^{\dagger}\) and \(a\) are the Fermionic creation and annihilation operators and \(h_{ij}\) and \(h_{ijkl}\) are the one- and two- body electronic integrals respectively. The integrals are obtained from mean-field calculations, such as Hartree-Fock. For more details see e.g. [4, 5]

In order to build a computable, one must InQuantize the chemical system. This refers to how InQuanto takes a chemical system defined by the atomic coordinates or some model and constructs its set of qubit states and operators. Broadly, this can be considered to split into two steps, i) preparing mean-field quantities, and ii) selecting and representing the electronic system.

Doing so will allow us to construct and run computables and algorithms.

Preparing Mean-Field Systems

One must first process the molecule/material from a specification of molecular geometry or an atomic structure file (e.g. Then, drivers run mean-field calculations with a small classical computational overhead, such as Hartree-Fock.

Geometry takes the structure and loads it into InQuanto. Symmetry contains a set of tools for reducing the computational complexity of chemical systems at the structural, electronic, and qubit levels. Embeddings (e.g. DMET) allow one to focus computational effort on a part of the system, reducing the overall cost. Drivers are used to run classical computational chemistry calculations to construct components and are generally provided by InQuanto Extensions but there are also model Hamiltonians and data in Express.

Spaces, Operators, States and Mappings

When the mean-field system is defined and the classical components calculated, one can specify the Spaces, Operators, and States of the system and perform Qubit Mappings.

For example, systems of correlated electrons are modelled using some electronic Hamiltonian operator which acts on a Fermionic Hilbert space, with the state often being defined by a set of occupation numbers. In InQuanto we can construct these spaces, operators, and states and then convert them to qubit spaces, qubit operators, and qubit states.

Many quantum algorithms for quantum chemistry require the preparation of an ansatz state, which may be parameterized. These ansatzes are educated guesses for the state of the chemical system. InQuanto represents the generation of quantum circuits necessary for a variety of ansatzes using the ansatz classes.

Running Computables and Algorithms

When the qubit based ansatz and operators have been prepared, they are fed into Computables and we are ready to focus on exactly how the computable is evaluated. This is done using Protocols. Specifically, Protocols add instructions for how to measure the necessary state and operators for the computable of interest. They are also where noise mitigation capabilities may be provided.

Computables and Protocols are fed into the algorithm along with some complementary initial parameters. The initial parameters for the qubit states vary between algorithms. Similarly, the form of the ‘solver’ also varies between algorithms. If performing a variational algorithm then the preference is for an efficient Minimizers, whilst time-evolution algorithms require Integrators.

The last component we need to build an algorithms or computables class is quantum computational hardware and simulators accessed via pytket-extensions. Pytket optimizes the underlying circuit for performance, can deliver the circuit to the hardware or simulator (when provided credentials), and will collect the processed circuit results to pass to InQuanto.

Having provided the algorithms with the necessary input, all that remains is to run the circuit(s). This will automatically pass the information from the built algorithms to the backend, queue then run the experiment, and return results. The algorithms object can then be inquired for results, for example algorithm.final_values, which correspond to the computable and gives the chemical quantity of interest.

Expert use of InQuanto

For expert quantum computational chemistry users there are a couple of useful tips.

There are a number of fully customizable classes which allow users to construct objects from scratch or modify prebuilt objects. For example, QubitMapping can be used to build your own mapping, or operators classes have many tools for adding, removing, or manipulating terms.

Expert users can also manipulate circuits using the pytket stack. Ultimately, InQuanto constructs, runs, and interprets pytket circuits. Thus, one can obtain the circuit objects from InQuanto using functions such as get_circuit() to change the underlying circuit e.g. by manually appending gates. It is also possible to inject pytket native objects into InQuanto, such as passing a custom built compiler pass objects to protocols. Due to its modular nature, these modifications can be made and become part of an InQuanto workflow.