Loops and Strings in a Superconducting Lattice Gauge Simulator

TL;DR

This paper presents a superconducting circuit architecture for simulating 2+1D lattice gauge theories, demonstrating confinement phenomena through nonlocal order parameters and tunable coupling regimes.

Contribution

It introduces a novel superconducting fluxonium-based quantum simulator for U(1) lattice gauge theory, including methods to engineer Gauss's law and measure nonlocal operators.

Findings

Numerical evidence of the confined phase in the ground state.

Implementation of nonlocal order parameters like Wilson loops and 't Hooft strings.

Tunable coupling regimes between strong and intermediate coupling.

Abstract

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1 representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.