Protecting Quantum Simulations of Lattice Gauge Theories through Engineered Emergent Hierarchical Symmetries

TL;DR

This paper introduces a Floquet-engineering approach to enhance the stability of quantum simulations of lattice gauge theories by creating emergent hierarchical symmetries that suppress violations of local constraints.

Contribution

It develops a method to protect gauge symmetries in quantum simulations through engineered emergent hierarchies, improving the lifetime of the simulated states.

Findings

Numerical verification for 1D U(1) quantum link model confirms the theory.

Defects violating gauge constraints are kinetically constrained and less mobile.

Emergent symmetries create a hierarchy of state lifetimes, enhancing simulation stability.

Abstract

We present a strategy for the quantum simulation of many-body lattice models with constrained Hilbert spaces. We focus on lattice gauge theories (LGTs), which underlie a wide range of phenomena in particle physics, condensed matter, and quantum information. In present-day quantum computing platforms, perfect restrictions of the Hilbert space to the desired gauge sectors are beyond reach: for LGTs, violations of the local constraint are unavoidable, posing a formidable challenge for the emulation of the underlying physics. Here, we develop a Floquet-engineering framework that restructures departures from a target sector such that a series of emergent local symmetries occurs hierarchically in time and in a controllable way. This leads to a set of approximate dynamical selection rules that strongly restrict inter-sector couplings, resulting in a pronounced, symmetry-controlled hierarchy of lifetimes for the state population to spread among sectors. Concretely, this protects $U(1)$ LGTs against violations of the {defining} local symmetry. While some sectors remain very long-lived, others are destabilized on shorter timescales. We numerically verify our theory for the one-dimensional $U(1)$ quantum link model. In addition, we reveal that `defects', whose movement accounts for violations of the gauge constraint, are kinetically constrained, becoming mobile only through the assistance of intra-sector dynamics, which we describe using an effective quantum marble model. Our results can thus be used to extend the lifetime, in the spirit of passive error correction, of quantum simulations of complex many-body problems when emergent or desired local symmetries are only implemented approximately.