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DY: Fachverband Dynamik und Statistische Physik

DY 9: Focus Session: Quantum Interactive Dynamics II (joint session DY/TT)

DY 9.6: Talk

Monday, March 18, 2024, 17:00–17:15, A 151

Quantum simulation of the 1D Fermi-Hubbard model as a Z2 lattice-gauge theory — •Uliana Khodaeva¹, Dmitry Kovrizhin², and Johannes Knolle^{1, 3, 4} — ¹Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany — ²LPTM, CY Cergy Paris Universite, UMR CNRS 8089, Pontoise 95032 Cergy-Pontoise Cedex, France — ³Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany — ⁴Blackett Laboratory, Imperial College of London, London SW7 2AZ, United Kingdom

The Fermi-Hubbard model is one of the central paradigms in the physics of strongly-correlated quantum many-body systems. Here we propose a quantum circuit algorithm based on the Z2 lattice gauge theory (LGT) representation of the one-dimensional Fermi-Hubbard model, which is suitable for implementation on current NISQ quantum computers. Within the LGT description there is an extensive number of local conserved quantities commuting with the Hamiltonian. We show how these conservation laws can be used to implement an efficient error-mitigation scheme. The latter is based on a post-selection of states for noisy quantum simulators. While the LGT description requires a deeper quantum-circuit compared to a Jordan-Wigner (JW) based approach, remarkably, we find that our error-correction protocol leads to results being on-par with a standard JW implementation on noisy quantum simulators.

Keywords: The Fermi-Hubbard model; Lattice gauge theory; Error-mitigation scheme; Noisy quantum simulators; NISQ quantum computers