Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

TL;DR

This paper proposes using superconducting quantum circuits to simulate two-dimensional U(1) lattice gauge theories, enabling the study of complex quantum phases and dynamics that are challenging for classical computation.

Contribution

It introduces a method to engineer gauge-invariant Hamiltonians in superconducting circuits, facilitating the simulation of quantum gauge theories and their phenomena.

Findings

Small circuit lattices can demonstrate electric flux string dynamics.

Superconducting technology can implement complex gauge interactions.

Simulations remain feasible despite decoherence and disorder effects.

Abstract

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.