Spin Exchange-Enabled Quantum Simulator for Large-Scale Non-Abelian Gauge Theories

Abstract

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <a:mi>SU</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>N</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <f:mrow> <f:mi mathvariant="normal">U</f:mi> </f:mrow> <f:mo stretchy="false">(</f:mo> <f:mi>N</f:mi> <f:mo stretchy="false">)</f:mo> </f:math> LGTs with dynamical matter in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <l:mi>d</l:mi> <l:mo>+</l:mo> <l:mn>1</l:mn> <l:mrow> <l:mrow> <l:mi mathvariant="normal">D</l:mi> </l:mrow> </l:mrow> </l:math> , enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <p:mn>2</p:mn> <p:mo>+</p:mo> <p:mn>1</p:mn> <p:mrow> <p:mrow> <p:mi mathvariant="normal">D</p:mi> </p:mrow> </p:mrow> <p:mspace width="0.2em"/> <p:mi>SU</p:mi> <p:mo stretchy="false">(</p:mo> <p:mn>2</p:mn> <p:mo stretchy="false">)</p:mo> </p:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <w:mrow> <w:mi mathvariant="normal">U</w:mi> </w:mrow> <w:mo stretchy="false">(</w:mo> <w:mn>2</w:mn> <w:mo stretchy="false">)</w:mo> </w:math> LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024

Topics & Concepts