Variational solutions to fermion-to-qubit mappings in two spatial dimensions
Jannes Nys, Giuseppe Carleo
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 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>&#x003E;</mml:mo></mml:math>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>V</mml:mi></mml:math>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.