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.

References in corpus (4)

• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• Determinant-free fermionic wave function using feed-forward neural networks
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions

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• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
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