Gauge protection in non-Abelian lattice gauge theories

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 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 \textit{adjusted} gauge theory with the same local gauge symmetry up to least a timescale $\propto \sqrt{V/V_0^3}$. Thereafter, a \textit{renormalized} gauge theory dominates up to a timescale $\propto \exp (V/V_0)/V_0$ 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 exact diagonalization, 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 NISQ devices.

24 pages, 7 figures, journal article

References in corpus (11)

• Probing many-body dynamics on a 51-atom quantum simulator
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Quantum simulation of the Schwinger model: A study of feasibility
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Gauge symmetry from decoupling
• Suppressing Coherent Gauge Drift in Quantum Simulations

Cited by in corpus (33)

• Quantum Simulation for High Energy Physics
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Bounds in Nonequilibrium Quantum Dynamics
• Stabilizing lattice gauge theories through simplified local pseudo generators
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Probing confinement in a ${\mathbb{Z}}_2$ lattice gauge theory on a quantum computer
• Engineering a U(1) lattice gauge theory in classical electric circuits
• Projection algorithm for state preparation on quantum computers
• From square plaquettes to triamond lattices for SU(2) gauge theory
• Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Gauge Theory Couplings on Anisotropic Lattices
• Dynamical quantum phase transitions in a noisy lattice gauge theory
• Disorder-free localization with Stark gauge protection
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Randomized measurement protocols for lattice gauge theories
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints