Real-Time Observation of Aharonov-Bohm Interference in a $\mathbb{Z}_2$ Lattice Gauge Theory on a Hybrid Qubit-Oscillator Quantum Computer

TL;DR

This paper demonstrates a novel hybrid quantum simulation of a $ ext{Z}_2$ lattice gauge theory using a trapped-ion device, observing Aharonov-Bohm interference with dynamical gauge fields in a quasi-2D setup.

Contribution

It introduces a resource-efficient encoding of a $ ext{Z}_2$ lattice gauge theory on a hybrid qubit-oscillator quantum computer, combining digital and analogue techniques for real-time evolution.

Findings

First observation of Aharonov-Bohm interference with dynamical gauge fields.

Experimental probing of gauge-invariant dynamics obeying Gauss's law.

Extension to higher-dimensional lattice geometries using synthetic dimensions.

Abstract

Quantum simulations of lattice gauge theories (LGTs) with both dynamical matter and gauge fields provide a promising approach to studying strongly coupled problems beyond classical computational reach. Yet, implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here, we demonstrate a resource-efficient encoding of a $\mathbb{Z}_2$ LGT using a hybrid qubit-oscillator trapped-ion quantum device, where qubits represent gauge fields and vibrational modes naturally encode bosonic matter fields. This architecture utilises synthetic dimensions to construct higher-dimensional lattice geometries and combines digital and analogue techniques to prepare initial states, realise gauge-invariant real-time evolution, and measure the relevant observables. We experimentally probe dynamics obeying Gauss's law in a $\mathbb{Z}_2$ link and extend this to a loop geometry, marking the first steps towards higher-dimensional LGTs. In this quasi-2D setup, we observe Aharonov-Bohm interference for the first time with dynamical gauge fields encoding magnetic flux, demonstrating the interplay between charge and flux. Our results chart a promising path for scalable quantum simulations of bosonic gauge theories and outline a roadmap for realising exotic LGTs in higher dimensions.