Contextual Subspace Variational Quantum Eigensolver

We describe the contextual subspace variational quantum eigensolver (CS-VQE), an approximation method based on the standard variational quantum eigensolver (VQE). CS-VQE obtains a classical approximation to the ground state energy by solving a hidden variables model for a noncontextual approximation to the Hamiltonian. This approximation is then used to construct a smaller VQE instance that computes quantum corrections to this classical approximation in a contextual subspace. CS-VQE is an example of a genuinely hybrid NISQ algorithm in the sense that part of the answer is computed on the classical computer and part of the answer on the quantum computer.