Some Conceptual Aspects of Operator Design for Quantum Simulations of Non-Abelian Lattice Gauge Theories

TL;DR

This paper explores how quantum numbers and entanglement are managed in quantum simulations of non-Abelian lattice gauge theories, proposing methods to reduce quantum resources while maintaining gauge invariance.

Contribution

It introduces a novel approach to generate necessary entanglement through operator delocalization, enabling resource-efficient quantum simulations of lattice gauge theories.

Findings

Entanglement is generated via delocalized operators with nearest-neighbor controls.

Hybridization with qudits or qubits reduces quantum resource requirements.

The approach maintains gauge invariance during time evolution.

Abstract

In the Kogut-Susskind formulation of lattice gauge theories, a set of quantum numbers resides at the ends of each link to characterize the vertex-local gauge field. We discuss the role of these quantum numbers in propagating correlations and supporting entanglement that ensures each vertex remains gauge invariant, despite time evolution induced by operators with (only) partial access to each vertex Hilbert space. Applied to recent proposals for eliminating vertex-local Hilbert spaces in quantum simulation, we describe how the required entanglement is generated via delocalization of the time evolution operator with nearest-neighbor controls. These hybridizations, organized with qudits or qubits, exchange classical operator preprocessing for reductions in quantum resource requirements that extend throughout the lattice volume.