Variational Algorithms

Variational algorithms optimize cost functions to produce meaningful quantum states. For example the ground state wave function is known to be the one with lowest total energy, and therefore for a parametric circuit, the symbol values can be tuned until the lowest possible energy is found. This is the idea behind the Variational Quantum Eigensolver, which is a popular method for quantum computational chemistry on current hardware due to its low circuit depth. These are hybrid algorithms which perform the parameter optimization steps on a classical computer using minimizers. Other variational algorithms, such as Variational Quantum Deflation optimize different cost functions to resolve excited states. Finally, the various flavors of ADAPT-VQE iteratively improve the circuit as well as the parameters values.