A Non-Orthogonal Variational Quantum Eigensolver
ORAL
Abstract
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).
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Presenters
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William Huggins
Chemistry, University of California, Berkeley, University of California, Berkeley
Authors
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William Huggins
Chemistry, University of California, Berkeley, University of California, Berkeley
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Joonho Lee
University of California, Berkeley, Department of Chemistry, Columbia University, Chemistry, Columbia University
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Unpil Baek
University of California, Berkeley, Physics, University of California, Berkeley
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Bryan O'Gorman
University of California, Berkeley, Electrical Engineering and Computer Sciences, University of California, Berkeley, QuAIL, Berkeley University, NASA
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Birgitta K Whaley
Chemistry, University of California, Berkeley, University of California, Berkeley, Department of Chemistry, University of California, Berkeley