Analysis of the confinement string in (2 + 1)-dimensional Quantum Electrodynamics with a trapped-ion quantum computer

TL;DR

This paper demonstrates how a trapped-ion quantum computer can simulate (2+1)-dimensional lattice QED, accurately measuring static potentials and visualizing confinement phenomena, advancing quantum simulation of complex gauge theories.

Contribution

It introduces a resource-efficient variational quantum algorithm for simulating lattice QED and validates it on a trapped-ion quantum device, capturing confinement and string breaking effects.

Findings

Quantum experiments agree with classical simulations for 10 and 24 qubits.

The method visualizes electric flux configurations in different regimes.

Results show potential for solving higher-dimensional gauge theories with quantum computers.

Abstract

Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a (2+1)-dimensional lattice discretization of Quantum Electrodynamics with the inclusion of dynamical fermionic matter. We define a suitable quantum algorithm to measure the static potential as a function of the distance between two charges on the lattice and we use a variational quantum calculation to explore the Coulomb, confinement and string breaking regimes. A symmetry-preserving and resource-efficient variational quantum circuit is employed to prepare the ground state of the theory at various values of the coupling constant, corresponding to different physical distances, allowing the accurate extraction of the static potential from a quantum computer. We demonstrate that results from quantum experiments on the Quantinuum H1-1 trapped-ion device and emulator, with full connectivity between qubits, agree with classical noiseless simulations using circuits with 10 and 24 qubits. Moreover, we visualize the electric field flux configurations that mostly contribute in the wave-function of the quantum ground state in the different regimes of the potential, thus giving insights into the mechanisms of confinement and string breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.