[Paper Review] Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators

Maarten Van Damme, Julius Mildenberger+3 more|arXiv (Cornell University)|Oct 13, 2021

Quantum and electron transport phenomena2 references4 citations

TL;DR

This paper proposes using local pseudogenerators—Hamiltonian terms that mimic the full gauge-symmetry generator only within the target gauge sector—to suppress nonperturbative gauge errors in lattice gauge theories. Through infinite matrix product state (iMPS) simulations and quantum circuit modeling, it demonstrates that this scheme stabilizes gauge invariance in the thermodynamic limit for all accessible evolution times, even with strong, nonperturbative errors, and reveals an emergent gauge symmetry beyond analytic predictions.

ABSTRACT

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. In a recent work [J. C. Halimeh extit{et al.}, arXiv:2108.02203], an experimentally feasible gauge-protection scheme has been proposed that is based on the concept of a extit{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 extit{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 NISQ devices.

Motivation & Objective

• To address the challenge of preserving gauge symmetry in analog quantum simulators of lattice gauge theories, especially under nonperturbative errors.
• To test whether local pseudogenerators—designed to act like the full gauge generator only in the target sector—can stabilize gauge invariance beyond perturbative regimes.
• To evaluate the performance of such schemes in the thermodynamic limit, where conventional analytic tools fail and experimental relevance is highest.
• To assess the feasibility and robustness of gauge protection using local pseudogenerators on finite NISQ-era quantum computers via Trotterized time evolution.
• To understand the role of noncompliant sequences in suppressing gauge violations and the emergence of effective gauge symmetry in large systems.

Proposed method

• Employing infinite matrix product state (iMPS) simulations to study quench dynamics in the thermodynamic limit, enabling access to long evolution times.
• Using noncompliant local pseudogenerator sequences $ c_j $ that are not globally consistent but are locally defined, allowing simulation in the thermodynamic limit.
• Applying the local pseudogenerator scheme via a modified Hamiltonian that penalizes gauge-symmetry-breaking terms through a sequence $ c_j $, which controls the strength and structure of the protection.
• Simulating gauge violation dynamics under nonperturbative errors (e.g., $ ilde{H}_1 $) and comparing results to finite-size exact diagonalization (ED) and experimental lifetimes.
• Conducting quantum circuit model simulations with Trotterization to validate the scheme on discrete, finite quantum computers.
• Analyzing the fraction $ \mathcal{R} $ of gauge-invariant sectors resonant with the target sector but differing locally, to assess the proliferation of gauge violations.

Experimental results

Research questions

• RQ1 Can local pseudogenerators suppress nonperturbative gauge errors in the thermodynamic limit, where perturbative approximations fail?
• RQ2 Does the gauge protection scheme based on local pseudogenerators lead to an emergent gauge symmetry in large systems, even beyond analytic predictions?
• RQ3 How does the performance of noncompliant pseudogenerator sequences compare to compliant ones in stabilizing gauge invariance in the thermodynamic limit?
• RQ4 To what extent does the fraction $ \mathcal{R} $ of resonant gauge-invariant sectors affect the spread of gauge violations in large systems?
• RQ5 Can the local pseudogenerator scheme be successfully implemented and stabilized on NISQ-era quantum computers using Trotterized time evolution?

Key findings

• The local pseudogenerator scheme successfully suppresses gauge violations to $ \propto \lambda^2 / V^2 $ for all accessible evolution times in the thermodynamic limit, even under nonperturbative errors.
• Gauge violation dynamics in the thermodynamic limit using the sequence $ c_j \in \{-1,3,-7,17\}/17 $ agree quantitatively with finite-size results for $ L=4 $ matter and gauge sites, indicating robustness.
• The fraction $ \mathcal{R} $ of gauge-invariant sectors resonant with the target sector decreases with system size, following an almost power-law decay, which slows the proliferation of gauge violations.
• The sequence $ c_j \in \{-1,3,-7,17\}/17 $ suppresses up to second-order gauge-breaking processes, outperforming the $ c_j = [6(-1)^j + 5]/11 $ sequence that only controls first-order processes.
• In iMPS simulations, gauge violations initially grow as $ \propto \lambda^2 t^2 $, then plateau at $ \propto \lambda^2 / V^2 $, and only later diverge from finite-size ED results at the largest accessible times, suggesting experimental relevance.
• Quantum circuit simulations confirm that the local pseudogenerator scheme suppresses gauge violations on finite quantum computers using Trotterized time evolution, validating its feasibility for NISQ devices.