Simulating a low-weight encoding of the Fermi-Hubbard Model with QAOA

ORAL

Abstract

Recent work [1] has proposed a compact fermion-to-qubit mapping for the Fermi-Hubbard model (FHM), potentially lowering the overhead needed to simulate such a system on quantum hardware. In prior work [2], we numerically investigated how well a quantum annealer could prepare ground states of the FHM encoded using the resource-efficient mapping. In order to compare these results to gate-model systems, we turn to a QAOA-style approach and replace the annealing schedule with both Trotterizations thereof and also more general Hamiltonian-variational ansatze based on the terms of the mapped FH Hamiltonian. We investigate the achievable ground state fidelities of these gate sequences, consider various optimizations of the ansatze structure, and offer resource estimations of the optimized QAOA protocols for near-term hardware.

[1] Derby, Klassen, Bausch, Cubitt, Phys. Rev. B 104, 035118

[2] Levy et al. arXiv:2207.14374v1

*We are grateful for support from NASA Ames Research Center, NAMS Contract No. NNA16BD14C, and from the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE- SC0012704 including through NASA-DOE interagency agreement SAA2-403601.

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Presenters

  • Joseph Barreto

    • USC, QuAIL, USRA, NASA

Authors

  • Joseph Barreto

    • USC, QuAIL, USRA, NASA

  • Ryan Levy

    • Center for Computational Quantum Physics, Flatiron Institute

  • Lucas Brady

    • QuAIL, USRA, NASA
    • National Institute of Standards and Tech

  • Zoe Gonzalez Izquierdo

    • QuAIL, USRA, NASA
    • USRA - Univ Space Rsch Assoc

  • Jeffrey S Marshall

    • QuAIL, USRA, NASA

  • Eleanor G Rieffel

    • QuAIL, NASA
    • NASA Ames Research Center

  • Zhihui Wang

    • QuAIL, USRA, NASA
    • USRA - Univ Space Rsch Assoc

  • Filip Wudarski

    • QuAIL, USRA, NASA