Truncation-Free Quantum Simulation of Pure-Gauge Compact QED Using Josephson Arrays

TL;DR

This paper introduces a truncation-free quantum simulation method for lattice QED using Josephson arrays, enabling more accurate and feasible analog simulations of gauge theories with superconducting circuits.

Contribution

The authors propose a novel truncation-free approach to simulate lattice QED with Josephson arrays, avoiding the common Hilbert space truncation in quantum simulations.

Findings

Simulates quasi-2D systems with up to 2×N plaquettes.

Provides an approximate method for fully-2D theory.

Lays groundwork for continuous gauge group simulations.

Abstract

Quantum simulation is one of the methods that have been proposed and used in practice to bypass computational challenges in the investigation of lattice gauge theories. While most of the proposals rely on truncating the infinite dimensional Hilbert spaces that these models feature, we propose a truncation-free method based on the exact analogy between the local Hilbert space of lattice QED and that of a Josephson junction. We provide several proposals, mostly semi-analog, arranged according to experimental difficulty. Our method can simulate a quasi-2D system of up to $2\times N$ plaquettes, and we present an approximate method that can simulate the fully-2D theory, but is more demanding experimentally and not immediately feasible. This sets the ground for analog quantum simulation of lattice gauge theories with superconducting circuits, in a completely Hilbert space truncation-free procedure, for continuous gauge groups.