Quantum computation of SU(2) lattice gauge theory with continuous variables

TL;DR

This paper introduces a continuous-variable quantum computing framework for simulating SU(2) lattice gauge theories, enabling the study of non-Abelian gauge dynamics beyond qubit-based methods.

Contribution

It develops a novel continuous-variable approach for SU(2) lattice gauge theory, including gauge fixing and Hamiltonian simulation techniques.

Findings

Feasibility of simulating non-Abelian gauge theories with continuous variables

Demonstration of computing system dynamics and ground states

Potential for exploring real-time quantum field theory dynamics

Abstract

We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as a two-dimensional grid of plaquettes, detailing the use of gauge fixing to reduce the degrees of freedom and simplify the Hamiltonian. We demonstrate how the system dynamics, ground states, and energy gaps can be computed using the continuous-variable approach to quantum computing. Our results indicate that it is feasible to study non-Abelian gauge theories with continuous variables, providing new avenues for understanding the real-time dynamics of quantum field theories.