• Open Access

Gauge-Symmetry Protection Using Single-Body Terms

Jad C. Halimeh, Haifeng Lang, Julius Mildenberger, Zhang Jiang, and Philipp Hauke
PRX Quantum 2, 040311 – Published 18 October 2021

Abstract

Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in U(1) lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times. Further, for few-body error terms, we show numerically that this is achieved with resources exhibiting little dependence on system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to t>1010/J for continuous time, with J the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital noisy intermediate-scale quantum devices.

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  • Received 6 July 2020
  • Revised 8 August 2021
  • Accepted 7 September 2021

DOI:https://doi.org/10.1103/PRXQuantum.2.040311

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsParticles & FieldsGeneral PhysicsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jad C. Halimeh1,*, Haifeng Lang1,2, Julius Mildenberger1, Zhang Jiang3, and Philipp Hauke1

  • 1INO-CNR BEC Center and Department of Physics, University of Trento, via Sommarive 14, Trento I-38123, Italy
  • 2Theoretical Chemistry, Institute of Physical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, Heidelberg 69120, Germany
  • 3Google AI Quantum, Venice, California, USA

  • *jad.halimeh@physik.lmu.de

Popular Summary

Scientists are currently developing a new generation of tabletop quantum devices that are set up to controllably simulate dynamics of elementary particles of nature. A major challenge in this effort is to ensure the simulation respects specific constraints, for which this paper develops a general and hardware-friendly scheme.

The dynamics of elementary particles such as electrons, positrons, quarks, and gluons is governed by gauge theories defined by local constraints. An example is Gauss’s law in quantum electrodynamics, which is responsible for the vanishing rest mass of the photon and the long-range Coulomb interaction between electric charges. The difficulty of solving gauge theories, however, often hampers our theoretical understanding of elementary particles. For this reason, laboratories worldwide are currently developing quantum simulators, i.e., high-precision devices such as quantum computers or ultracold atoms in lattices of light, to controllably investigate desired target models. The main challenge of quantum-simulating gauge theories is to enforce the defining local constraint. This paper develops a hardware-friendly way to achieve this by simple control pulses. Numerical benchmarks illustrate the excellent performance of the scheme, and a theoretical framework puts it onto a solid foundation and demonstrates exponential improvement over the state of the art. These results open the door towards large-scale and robust simulations of gauge theories in quantum hardware.

In the future, these may shed light onto fundamental questions as are investigated, e.g., in particle colliders, such as how quantum information spreads through a system of elementary particles, or how such models with strong constraints can thermalize after a perturbation.

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Vol. 2, Iss. 4 — October - December 2021

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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