In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems. It is a hybrid algorithm that uses both classical computers and quantum computers to find the ground state of a given physical system. Given a guess or ansatz, the quantum processor calculates the expectation value of the system with respect to an observable, often the Hamiltonian, and a classical optimizer is used to improve the guess. The algorithm is based on the variational method of quantum mechanics.
It was originally proposed in 2014, with corresponding authors Alberto Peruzzo, Alán Aspuru-Guzik and Jeremy O'Brien.[a][1][2] The algorithm has also found applications in quantum machine learning and has been further substantiated by general hybrid algorithms between quantum and classical computers.[3] It is an example of a noisy intermediate-scale quantum (NISQ) algorithm.
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