An efficient quantum algorithm for building effective Hamiltonians on fault-tolerant hardware

ORAL

Abstract

The construction of accurate effective Hamiltonians for interacting quantum systems is a long-standing problem in many-body quantum mechanics. We present a novel quantum algorithm for constructing effective Hamiltonians built upon the methodology of density matrix downfolding (DMD). We provide formal theoretical developments in downfolding, including the novel concept of Hamiltonian compressibility, show that a quantum implementation of DMD addresses the main systematic errors present in the classical implementation --- sampling of low-energy states in the physical theory --- and provide circuits for implementing DMD on fault-tolerant quantum hardware. We also provide rigorous resource estimates at the logical and physical level for the case of a doped 2-D Fermi-Hubbard model and a large cuprate supercell.

*This article has been co-authored by employees of National Technology & Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The authors own all right, title and interest in and to the article and are solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan url{https://www.energy.gov/downloads/doe-public-access-plan}.

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Presenters

  • Shivesh Pathak

    • Sandia National Lab

Authors

  • Shivesh Pathak

    • Sandia National Lab

  • Antonio E Russo

    • Sandia National Laboratories
    • Sandia National Lab

  • Alicia B Magann

    • Sandia National Laboratories

  • Eric Bobrow

    • Sandia National Lab

  • Stefan K Seritan

    • Sandia National Laboratories

  • Andrew J Landahl

    • Sandia National Laboratories

  • Andrew D Baczewski

    • Sandia National Laboratories