Compact U(1) Lattice Gauge Theory in Superconducting Circuits with Infinite-Dimensional Local Hilbert Spaces

TL;DR

This paper introduces a superconducting circuit design that simulates a compact U(1) lattice gauge theory using the natural infinite-dimensional Hilbert space of the circuit's variables, enabling scalable quantum simulation of gauge dynamics.

Contribution

It presents a novel superconducting circuit architecture that encodes gauge and matter fields directly, with exact Gauss's law and microscopic gauge-matter coupling, without truncation or auxiliary elements.

Findings

Numerical simulations confirm emergence of compact electrodynamics and vortex excitations.

Circuit parameters are feasible with current technology.

The platform enables scalable analog quantum simulation of non-perturbative gauge theories.

Abstract

We propose a superconducting-circuit architecture that realizes a compact U(1) lattice gauge theory using the intrinsic infinite-dimensional Hilbert space of phase and charge variables. The gauge and matter fields are encoded directly in the degrees of freedom of the rotor variables associated with the circuit nodes, and Gauss's law emerges exactly from the conservation of local charge, without auxiliary stabilizers, penalty terms, or Hilbert-space truncation. A minimal gauge-matter coupling arises microscopically from Josephson nonlinearities, whereas the magnetic plaquette interaction is generated perturbatively via virtual matter excitations. Numerical diagonalization confirms the emergence of compact electrodynamics and coherent vortex excitations, underscoring the need for large local Hilbert spaces in the continuum regime. The required circuit parameters are within the current experimental capabilities. Our results establish superconducting circuits as a scalable, continuous-variable platform for analog quantum simulation of non-perturbative gauge dynamics.