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

Jannes Nys and Giuseppe Carleo

École Polytechnique Fédérale de Lausanne (EPFL), Institute of Physics, CH-1015 Lausanne, Switzerland
Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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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 ($\gt$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.

One can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional (gauge) constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations.

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Cited by

[1] Filippo Vicentini, Damian Hofmann, Attila Szabó, Dian Wu, Christopher Roth, Clemens Giuliani, Gabriel Pescia, Jannes Nys, Vladimir Vargas-Calderon, Nikita Astrakhantsev, and Giuseppe Carleo, "NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems", arXiv:2112.10526.

[2] Adam Wyrzykowski, "Local spin description of fermions on a lattice", arXiv:2206.10393.

[3] Jannes Nys and Giuseppe Carleo, "Quantum circuits for solving local fermion-to-qubit mappings", arXiv:2208.07192.

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