[Paper Review] Stabilizing Gauge Theories in Quantum Simulators: A Brief Review

Jad C. Halimeh, Philipp Hauke|arXiv (Cornell University)|Apr 28, 2022

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper reviews linear gauge protection schemes that stabilize U(1) and Z2 gauge symmetries in quantum simulators by projecting onto the physical subspace using local generators. The method enables robust simulation of exotic non-equilibrium phenomena like quantum many-body scars and disorder-free localization, with experimental validation in Rydberg atoms and ultracold atoms, achieving stable gauge symmetry over 15 Trotter steps at V=6J.

ABSTRACT

Quantum simulation is at the heart of the ongoing "second" quantum revolution, with various synthetic quantum matter platforms realizing evermore exotic condensed matter and particle physics phenomena at high levels of precision and control. The implementation of gauge theories on modern quantum simulators is especially appealing due to three main reasons: (i) it offers a new probe of high-energy physics on low-energy tabletop devices, (ii) it allows exploring condensed matter phenomena that are prominent in gauge theories even without a direct connection to high-energy physics, and (iii) it serves as a banner of experimental benchmarking given the plethora of local constraints arising from the gauge symmetry that need to be programmed and controlled. In order to faithfully model gauge-theory phenomena on a quantum simulator, stabilizing the underlying gauge symmetry is essential. In this brief review, we outline recently developed experimentally feasible methods introduced by us that have shown, in numerical and experimental benchmarks, reliable stabilization of quantum-simulator implementations of gauge theories. We explain the mechanism behind these extit{linear gauge protection} schemes, and illustrate their power in protecting salient features such as gauge invariance, disorder-free localization, quantum many-body scars, and other phenomena of topical interest. We then discuss their application in experiments based on Rydberg atoms, superconducting qubits, and in particular ultracold neutral atoms in optical superlattices. We hope this review will illustrate some facets of the exciting progress in stabilization of gauge symmetry and in gauge-theory quantum simulation in general.

Motivation & Objective

• To address the challenge of maintaining gauge symmetry in quantum simulators where gauge invariance is not hardwired into the Hamiltonian.
• To develop experimentally feasible stabilization protocols that preserve physical consistency in lattice gauge theories.
• To enable the simulation of exotic far-from-equilibrium phenomena such as quantum many-body scars and disorder-free localization.
• To demonstrate the effectiveness of linear gauge protection in realistic platforms like Rydberg atoms, superconducting qubits, and ultracold atoms in optical superlattices.
• To explore the physical implications of gauge-symmetry violation as a source of new dynamics, such as staircase prethermalization.

Proposed method

• The method employs a linear gauge protection term proportional to the local U(1) Gauss’s law generator, which projects the system into the physical subspace.
• The protection Hamiltonian is constructed using the local generator of gauge symmetry, ensuring that only gauge-invariant states are energetically favored.
• The scheme uses only single-qubit gates, minimizing experimental overhead and enabling implementation in near-term quantum devices.
• It is formulated both in terms of the local generator and a pseudogenerator, allowing flexibility in implementation and analysis.
• The approach stabilizes the gauge symmetry dynamically during time evolution, preventing drift into unphysical states.
• Numerical and experimental benchmarks confirm that the method maintains gauge invariance over multiple Trotter steps, even with moderate coupling strength.

Experimental results

Research questions

• RQ1 How can gauge symmetry be stabilized in quantum simulators without hardcoding Gauss’s law into the Hamiltonian?
• RQ2 What are the minimal experimental resources required to stabilize U(1) and Z2 gauge theories in quantum simulators?
• RQ3 Can linear gauge protection preserve non-equilibrium quantum phenomena such as quantum many-body scars and disorder-free localization?
• RQ4 How does gauge-symmetry violation influence the emergence of long-lived prethermal states in driven systems?
• RQ5 What are the implications of gauge-symmetry breaking for the dynamics of strongly correlated systems in quantum simulators?

Key findings

• The linear gauge protection scheme successfully stabilizes U(1) gauge symmetry over 15 Trotter steps in a Rydberg atom experiment using only single-qubit gates and a moderate coupling strength of V=6J.
• The method preserves key physical features such as gauge invariance, quantum many-body scars, and disorder-free localization in the presence of perturbations.
• A transition from Z2 to effective U(1) gauge symmetry leads to a drastic suppression of dynamics due to stronger constraints from Gauss’s law.
• The scheme enables the observation of novel phenomena such as staircase prethermalization, where small gauge-symmetry-breaking terms induce a sequence of long-lived prethermal plateaus.
• The approach is experimentally viable in multiple platforms, including ultracold atoms in optical superlattices, Rydberg atoms, and superconducting qubits, with minimal overhead.
• The results demonstrate that gauge-symmetry violation is not merely an error source but can generate new physical phenomena, such as slow dynamics in superpositions of different gauge sectors.