Related papers: Quantum simulation of the 1D Fermi-Hubbard model as a $\mathrm{Z}

Quantum simulation of the 1D Fermi-Hubbard model as a $\mathrm{Z}_2$ lattice-gauge theory

URL: http://arxiv.org/abs/2305.04648v4
Date: Wed, 8 Nov 2023 10:52:16 GMT
Title: Quantum simulation of the 1D Fermi-Hubbard model as a $\mathrm{Z}_2$ lattice-gauge theory
Authors: Uliana E. Khodaeva, Dmitry L. Kovrizhin, and Johannes Knolle
Abstract summary: We propose a quantum circuit algorithm based on the Fermi-Hubbard model. We show how these conservation laws can be used to implement an efficient error-mitigation scheme.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 $\mathrm{Z}_2$ 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.

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