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arXiv:2203.10927 · Physical review. B./Physical review. B

Dynamical quantum phase transitions in a noisy lattice gauge theory

Rasmus Berg Jensen, Simon Panyella Pedersen, Nikolaj Thomas Zinner

Published Jun 16, 2022• 20 citations
arXivHTMLPDF

Abstract

Lattice gauge theories form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of engineered quantum devices providing new tools to study, e.g., dynamics of such theories. The massive Schwinger model is known to exhibit intricate properties of more complicated theories and has recently been shown to undergo dynamical quantum phase transitions out of equilibrium. With current technology, noise is inevitable and potentially fatal for a successful quantum simulation. This paper studies the dynamics subject to noise of a $(1+1)\mathrm{D}\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)$ quantum link model following a quench of the sign of the mass term. We find that not only is the system capable of handling noise at rates realistic in NISQ-era devices, promising the possibility to study the target dynamics with current technology, but the effect of noise can be understood in terms of simple models. Specifically the gauge-breaking nature of bit flip channels results in exponential dampening of state amplitudes, and thus observables, which does not affect the structures of interest. This is especially important as it demonstrates that the gauge theory can be successfully studied with devices that only exhibit approximate gauge invariance.

DOI
10.1103/physrevb.105.224309

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Lattice gauge theories form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of engineered quantum devices providing new tools to study, e.g., dynamics of such theories. The massive Schwinger model is known to exhibit intricate properties of more complicated theories and has recently been shown to undergo dynamical quantum phase transitions out of equilibrium. With current technology, noise is inevitable and potentially fatal for a successful quantum simulation. This paper studies the dynamics subject to noise of a (1+1)DU(1)(1+1)\mathrm{D}\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)(1+1)DU(1) quantum link model following a quench of the sign of the mass term. We find that not only is the system capable of handling noise at rates realistic in NISQ-era devices, promising the possibility to study the target dynamics with current technology, but the effect of noise can be understood in terms of simple models. Specifically the gauge-breaking nature of bit flip channels results in exponential dampening of state amplitudes, and thus observables, which does not affect the structures of interest. This is especially important as it demonstrates that the gauge theory can be successfully studied with devices that only exhibit approximate gauge invariance.
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We study the ground-state properties of a class of Zn{\mathbb{Z}}_{n}Zn​ lattice gauge theories in 1+11+11+1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the U(1) group, preserve the unitary character of the minimal coupling and have, therefore, the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-nnn limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper, we study the cases $n=2\textdiv{}8$ by means of a DMRG code that exactly implements Gauss's law. We perform a careful scaling analysis and show that, in absence of a background field, all Zn{\mathbb{Z}}_{n}Zn​ models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the CPCPCP symmetry. We then perform the large-nnn limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition of the zero-charge sector of the massive Schwinger model, which occurs at negative mass.
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. QLMs not only reproduce standard features of Wilson lattice gauge theories in equilibrium, but can also host new phenomena such as crystalline confined phases. The local constraints due to gauge invariance also provide kinetic restrictions that can influence substantially the real-time dynamics in these systems. We aim to characterize the nonequilibrium evolution in lattice gauge theories through the lens of dynamical quantum phase transitions, which provide general principles for real-time dynamics in quantum many-body systems. Specifically, we study quantum quenches for two representative cases, U(1) QLMs in (1+1)D and (2+1)D, for initial conditions exhibiting long-range order. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms.
An overarching goal in the flourishing field of quantum simulation for high-energy physics is the first-principles study of the microscopic dynamics of scattering processes on a quantum computer. Currently, this is hampered by small system sizes and a restriction to two-level representations of the gauge fields in state-of-the-art quantum simulators. Here, we propose efficient experimentally feasible digital qudit quantum circuits for far-from-equilibrium quench dynamics of a U(1)\mathrm{U}(1)U(1) quantum link lattice gauge theory, where the electric and gauge fields are represented as spin-111 operators. Using dedicated numerical simulations, we probe scattering processes in this model on these proposed circuits, focusing on meson-meson and meson-antimeson collisions. The latter are not possible with a two-level representation of the fields, highlighting the suitability of qudits in exploring scattering processes relevant to quantum electrodynamics. The probed scattering dynamics showcases rich physics, including meson flipping and a reflection-transmission transition in meson-antimeson collisions as a function of the gauge coupling strength. Our simulations, which include realistic noise models of dephasing and depolarization, show very good agreement with the exact noiseless dynamics, signaling the readiness of current qudit platforms to observe microscopic scattering dynamics with significantly shallower circuit depths than their qubit counterparts.
Simulating the real-time dynamics of gauge theories represents a paradigmatic use case to test the hardware capabilities of a quantum computer, since it can involve non-trivial input states' preparation, discretized time evolution, long-distance entanglement, and measurement in a noisy environment. We implemented an algorithm to simulate the real-time dynamics of a few-qubit system that approximates the Schwinger model in the framework of lattice gauge theories, with specific attention to the occurrence of a dynamical quantum phase transition. Limitations in the simulation capabilities on IBM Quantum were imposed by noise affecting the application of single-qubit and two-qubit gates, which combine in the decomposition of Trotter evolution. The experimental results collected in quantum algorithm runs on IBM Quantum were compared with noise models to characterize the performance in the absence of error mitigation.