Quantum simulations of quantum electrodynamics in Coulomb gauge

TL;DR

This paper proposes using Coulomb gauge in quantum simulations of lattice gauge theories to simplify the Hamiltonian and improve discretization, demonstrating feasibility through classical calculations of gauge observables.

Contribution

It introduces a Coulomb gauge-based discretization scheme for quantum lattice gauge theory simulations, enabling efficient mapping to qubits and preserving gauge constraints.

Findings

Polynomial scaling of qubits with system size

Successful calculation of U(1) plaquette and Wilson loop

Simplified gauge field discretization in Coulomb gauge

Abstract

In recent years, the quantum computing method has been used to address the sign problem in traditional Monte Carlo lattice gauge theory (LGT) simulations. We propose that the Coulomb gauge (CG) should be used in quantum simulations of LGT. This is because the redundant degrees of freedom can be eliminated in CG. Therefore, the Hamiltonian in CG does not need to be gauge invariance, allowing the gauge field to be discretized naively. We point out that discretized gauge fields and fermion fields should be placed on momentum and position lattices, respectively. Under this scheme, the CG condition and Gauss's law can be conveniently preserved by solving algebraic equations of polarization vectors. We also discuss the procedure for mapping gauge fields to qubits, and then demonstrate the polynomial scaling of qubits and the complexity of time evolution. Finally, we calculate the vacuum expectation value (VEV) of the U(1) plaquette operator and the Wilson loop on a classical device to test the performance of our discretization scheme.