Toward Quantum Simulation of SU(2) Gauge Theory using Non-Compact Variables

TL;DR

This paper introduces three key improvements in quantum simulation methods for SU(2) gauge theories, reducing resource requirements and enhancing scalability, validated through Monte Carlo benchmarks.

Contribution

It presents simplified Hamiltonians, efficient encoding with fewer qubits, and a method to lower scalar mass requirements, advancing quantum simulation of gauge theories.

Findings

Reduced circuit depth and qubit count for SU(2) simulations.

Monte Carlo benchmarks confirm improved simulation efficiency.

Validated noncompact variables as a scalable framework.

Abstract

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.