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  • Letter
  • Open Access

Efficient representation for simulating U(1) gauge theories on digital quantum computers at all values of the coupling

Christian W. Bauer1,* and Dorota M. Grabowska2,†

  • 1Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 2Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland

  • *cwbauer@lbl.gov
  • †dorota.grabowska@cern.ch
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Phys. Rev. D 107, L031503 – Published 21 February, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L031503

Abstract

We derive a representation for a lattice U(1) gauge theory with exponential convergence in the number of states used to represent each lattice site that is applicable at all values of the coupling. At large coupling, this representation is equivalent to the Kogut-Susskind electric representation, which is known to provide a good description in this region. At small coupling, our approach adjusts the maximum magnetic field that is represented in the digitization as in this regime the low-lying eigenstates become strongly peaked around zero magnetic field. Additionally, we choose a representation of the electric component of the Hamiltonian that gives minimal violation of the canonical commutation relation when acting upon low-lying eigenstates. For (2+1) dimensions with 4 lattice sites the expectation value of the plaquette operator can be calculated with only 7 states per lattice site with per-mille level accuracy for all values of the coupling constant.

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Phys. Rev. D 107, L031503– Published 21 February, 2023
  • Received 24 March 2022
  • Accepted 21 December 2022
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