Variational solutions to fermion-to-qubit mappings in two spatial dimensions

• URL: http://arxiv.org/abs/2205.00733v2
• Date: Wed, 5 Oct 2022 09:39:08 GMT
• Title: Variational solutions to fermion-to-qubit mappings in two spatial dimensions
• Authors: Jannes Nys, Giuseppe Carleo
• Abstract summary: We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the $t$-$V$ model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.

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