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arXiv:2403.14656

Stabilizing Quantum Simulators Of Gauge Theories Against $1/f$ Noise

Bhavik Kumar

Published Feb 26, 2024• 0 citations
arXivHTMLPDF

Abstract

This work investigates the application of quantum simulation in the ongoing "second" quantum revolution, which employs various synthetic quantum matter platforms, such as ultracold atoms in optical lattices, Rydberg atoms, and superconducting qubits, to realize exotic condensed matter and particle physics phenomena with high precision and control. Gauge theories are of particular interest in modern quantum simulators as they offer a new probe of high-energy physics on low-energy tabletop devices. However, to accurately model gauge-theory phenomena on a quantum simulator, stabilizing the underlying gauge symmetry is crucial. Through this thesis we demonstrate that a recently developed experimentally feasible scheme based on linear gauge protection, initially devised to protect against coherent gauge breaking errors, can also be used to suppress incoherent errors arising from $1/f^β$ noise prominent in various quantum simulation platforms. The Bloch-Redfield formalism is introduced to model gauge violations arising due to these incoherent errors given the noise power spectrum of the environment. The efficacy of linear gauge protection in stabilizing salient features of gauge theories in quantum simulators, such as gauge invariance and exotic far from equilibrium phenomenon focusing on disorder-free localization, and quantum many-body scars against $1/f^β$ noise sources, is illustrated. These results are immediately applicable in modern analog quantum simulators and digital NISQ devices, paving the way for further development in the field of quantum simulation of lattice gauge theories.

DOI
10.48550/arxiv.2403.14656

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Stabilizing Quantum Simulators Of Gauge Theories Against 1/f1/f1/f Noise
This work investigates the application of quantum simulation in the ongoing "second" quantum revolution, which employs various synthetic quantum matter platforms, such as ultracold atoms in optical lattices, Rydberg atoms, and superconducting qubits, to realize exotic condensed matter and particle physics phenomena with high precision and control. Gauge theories are of particular interest in modern quantum simulators as they offer a new probe of high-energy physics on low-energy tabletop devices. However, to accurately model gauge-theory phenomena on a quantum simulator, stabilizing the underlying gauge symmetry is crucial. Through this thesis we demonstrate that a recently developed experimentally feasible scheme based on linear gauge protection, initially devised to protect against coherent gauge breaking errors, can also be used to suppress incoherent errors arising from 1/fβ1/f^β1/fβ noise prominent in various quantum simulation platforms. The Bloch-Redfield formalism is introduced to model gauge violations arising due to these incoherent errors given the noise power spectrum of the environment. The efficacy of linear gauge protection in stabilizing salient features of gauge theories in quantum simulators, such as gauge invariance and exotic far from equilibrium phenomenon focusing on disorder-free localization, and quantum many-body scars against 1/fβ1/f^β1/fβ noise sources, is illustrated. These results are immediately applicable in modern analog quantum simulators and digital NISQ devices, paving the way for further development in the field of quantum simulation of lattice gauge theories.
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 \textit{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.
Suppression of 1/f1/f1/f noise in quantum simulators of gauge theories
In the current drive to quantum-simulate evermore complex gauge-theory phenomena, it is necessary to devise schemes allowing for the control and suppression of unavoidable gauge-breaking errors on different experimental platforms. Although there have been several successful approaches to tackle coherent errors, comparatively little has been done in the way of decoherence. By numerically solving the corresponding Bloch--Redfield equations, we show that the recently developed method of \textit{linear gauge protection} suppresses the growth of gauge violations due to 1/fβ1/f^β1/fβ noise as 1/Vβ1/V^β1/Vβ, where VVV is the protection strength and β>0β>0β>0, in Abelian lattice gauge theories, as we show through exemplary results for U(1)\mathrm{U}(1)U(1) quantum link models and Z2\mathbb{Z}_2Z2​ lattice gauge theories. We support our numerical findings with analytic derivations through time-dependent perturbation theory. Our findings are of immediate applicability in modern analog quantum simulators and digital NISQ devices.
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 gaugeinvariant 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 > 10 10 /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.
With recent progress in quantum simulations of lattice-gauge theories, it is becoming a pressing question how to reliably protect the gauge symmetry that defines such models. Recently, an experimentally feasible gauge-protection scheme has been proposed that is based on the concept of a local pseudogenerator, which is required to act identically to the full gauge-symmetry generator in the target gauge sector, but not necessarily outside of it. The scheme has been analytically and numerically shown to reliably stabilize lattice gauge theories in the presence of perturbative errors on finite-size analog quantum-simulation devices. In this work, through uniform matrix product state calculations, we demonstrate the efficacy of this scheme for nonperturbative errors in analog quantum simulators up to all accessible evolution times in the thermodynamic limit, where it is a priori neither established nor expected that this scheme will succeed. Our results indicate the presence of an emergent gauge symmetry in an adjusted gauge theory even in the thermodynamic limit, which is beyond our analytic predictions. Additionally, we show through quantum circuit model calculations that gauge protection with local pseudogenerators also successfully suppresses gauge violations on finite quantum computers that discretize time through Trotterization. Our results firm up the robustness and feasibility of the local pseudogenerator as a viable tool for enforcing gauge invariance in modern quantum simulators and noisy intermediate-scale quantum devices.
Abstract Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp(V/V 0)/V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.
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The stated overarching goal of the highly active field of quantum simulation of high-energy physics (HEP) is to achieve the capability to study \textit{ab-initio} real-time microscopic dynamics of 3+13+13+1D quantum chromodynamics (QCD). However, existing experimental realizations and theoretical proposals for future ones have remained restricted to one or two spatial dimensions. Here, we take a big step towards this goal by proposing a concrete experimentally feasible scalable cold-atom quantum simulator of a U(1)(1)(1) quantum link model of quantum electrodynamics (QED) in three spatial dimensions, employing \textit{linear gauge protection} to stabilize gauge invariance. Using tree tensor network simulations, we benchmark the performance of this quantum simulator through near- and far-from-equilibrium observables, showing excellent agreement with the ideal gauge theory. Additionally, we introduce a method for \textit{analog quantum error mitigation} that accounts for unwanted first-order tunneling processes, vastly improving agreement between quantum-simulator and ideal-gauge-theory results. Our findings pave the way towards realistic quantum simulators of 3+13+13+1D lattice gauge theories that can probe regimes well beyond classical simulability.