A Non-Orthogonal Variational Quantum Eigensolver*

We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for systematic improvement of a logical wavefunction ansatz without significant increase in circuit complexity. To minimize the circuit complexity, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. We propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of matrix elements and to adaptively schedule the required measurements. We apply these ideas to two strongly correlated systems, a square configuration of H₄ and the π-system of Hexatriene (C₆H₈).