Stabilizing lattice gauge theories through simplified local pseudo generators

Abstract

The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified \textit{local pseudogenerators} designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to timescales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multi-body full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the ${\mathbb{Z}}_2$ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.

Accepted version, 15 pages, 10 figures, 2 tables

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Thermalization dynamics of a gauge theory on a quantum simulator
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Quantum simulation of the Schwinger model: A study of feasibility
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Gauge protection in non-Abelian lattice gauge theories
• Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Gauge Theories with Ultracold Atoms
• Suppressing Coherent Gauge Drift in Quantum Simulations

Cited by in corpus (29)

• 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
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Bounds in Nonequilibrium Quantum Dynamics
• Constrained Optimization via Quantum Zeno Dynamics
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• $Abinitio$ derivation of lattice gauge theory dynamics for cold gases in optical lattices
• Disorder-free localization with Stark gauge protection
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Dynamical localization transition in the non-Hermitian lattice gauge theory
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories
• Confinement Induced Frustration in a One-Dimensional ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Interplay between lattice gauge theory and subsystem codes
• Quantum Simulation with Gauge Fixing: from Ising Lattice Gauge Theory to Dynamical Flux Model
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Quantum Simulation of QED in Coulomb Gauge
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Shearing approach to gauge-invariant Trotterization
• Robust quantum many-body scars in lattice gauge theories
• A digital Rydberg simulation of dynamical quantum phase transitions in the Schwinger model