Packaged Quantum States for Quantum Simulation of Lattice Gauge Theories

TL;DR

This paper introduces a gauge-invariant quantum state framework for simulating lattice gauge theories, ensuring physical states maintain correct gauge properties and are robust against certain errors.

Contribution

It develops a novel formalism using packaged quantum states that preserve gauge invariance and prevent fractional quantum numbers in quantum simulations of gauge theories.

Findings

Framework successfully applied to U(1), SU(2), and SU(3) theories

Provides explicit constructions and gauge-invariant measurement protocols

Suggests packaged states can reduce gauge-violating errors

Abstract

We develop a mathematical framework for the quantum simulation of lattice gauge theories using gauge-invariant packaged quantum states \cite{Ma2017,Ma2025}. In this formalism, every single excitation transforms as a complete \textbf{irreducible representation (irrep)} of the local gauge group, preventing any appearance of fractional or partial \textbf{internal quantum numbers (IQNs)}. Multi-particle excitations can form nontrivial packaged entangled states that are also gauge invariant, thereby forbidding partial or fractional IQNs. In other words, all IQNs of such packaged entangled states remain inseparably entangled. This ``packaging principle'' ensures that physical states remain confined to the correct gauge sector and excludes partial charges or colors, even when multiple excitations are entangled. We illustrate this approach for $\mathrm{U}(1)$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$ lattice gauge theories, discussing explicit constructions, Trotterized Hamiltonian evolution, and gauge-invariant measurements on a quantum simulator. We also outline how packaged states can mitigate gauge-violating errors and serve as natural building blocks for gauge-invariant coding schemes, while noting that standard quantum error correction is still required against typical local noise that respects gauge symmetry.