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).

*This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Algorithm Teams Program, and a Quantum Algorithms Focused Award from Google LLC B.O. was supported by a NASA Space Technology Research Fellowship.

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Presenters

  • William Huggins

    • Chemistry, University of California, Berkeley
    • University of California, Berkeley

Authors

  • William Huggins

    • Chemistry, University of California, Berkeley
    • University of California, Berkeley

  • Joonho Lee

    • University of California, Berkeley
    • Department of Chemistry, Columbia University
    • Chemistry, Columbia University

  • Unpil Baek

    • University of California, Berkeley
    • Physics, University of California, Berkeley

  • Bryan O'Gorman

    • University of California, Berkeley
    • Electrical Engineering and Computer Sciences, University of California, Berkeley
    • QuAIL, Berkeley University, NASA

  • Birgitta K Whaley

    • Chemistry, University of California, Berkeley
    • University of California, Berkeley
    • Department of Chemistry, University of California, Berkeley