Variational quantum eigensolver

The variational quantum eigensolver, usually shortened to VQE, is a hybrid quantum and classical algorithm for finding the lowest energy state of a physical system. A quantum processor prepares a trial state, called an ansatz, controlled by adjustable parameters, and measures the expectation value of an observable, most often the Hamiltonian of the system. A classical optimizer then uses that value to improve the parameters, and the loop repeats. The method rests on the variational principle of quantum mechanics, and it is applied to quantum chemistry, quantum simulation and optimization problems, where a cost function plays the part of the Hamiltonian. It was proposed in 2014 by a group including Alberto Peruzzo, Alan Aspuru-Guzik and Jeremy O'Brien, and it is a standard example of an algorithm designed for noisy intermediate-scale quantum hardware.