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

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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Cited by in corpus (11)

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• Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States
• Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Mott Transition and Volume Law Entanglement with Neural Quantum States
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Local fermion-to-qudit mappings: a practical recipe for four-level systems