Quantum Simulation of QED in Coulomb Gauge

TL;DR

This paper develops an efficient quantum algorithm for simulating Quantum Electrodynamics in Coulomb gauge on a lattice, reducing computational costs significantly compared to previous methods.

Contribution

It introduces a new position-space gauge field basis representation and a quantum algorithm that reduces gate complexity for real-time QED simulation.

Findings

Gate cost reduced by at least 10^8 times for modest lattice sizes.

Polynomial scaling of qubit and gate resources with lattice size and parameters.

Guarantees decoupling of unphysical gauge fields without constraints.

Abstract

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. Here we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green's function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of $10^8$ for modest lattice size and accuracy level compared with the previous work.