Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories

Abstract

Efficient quantum simulation protocols for any quantum theories demand efficient protection protocols for its underlying symmetries. This task is nontrivial for gauge theories as it is involves local symmetry/invariance. For non-Abelian gauge theories, protecting all the symmetries generated by a set of mutually non-commuting generators, is particularly difficult. In this letter, a global symmetry-protection protocol is proposed. Using the novel loop-string-hadron formalism of non-Abelian lattice gauge theory, we numerically demonstrate that all of the local symmetries get protected even for large time by this global symmetry protection scheme. With suitable protection strength, the dynamics of a (1+1)-dimensional SU(2) lattice gauge theory remains confined in the physical Hilbert space of the theory even in presence of explicit local symmetry violating terms in the Hamiltonian that may occur in both analog and digital simulation schemes as an error. The whole scheme holds for SU(3) gauge theory as well.

arXiv comment7 pages, 2 figures

References in corpus (79)

• Quantum Computing in the NISQ era and beyond
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator
• 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
• Lattice gauge theories simulations in the quantum information era
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Simulations of non-Abelian gauge theories with optical lattices
• Thermalization dynamics of a gauge theory on a quantum simulator
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
• QCD as a Quantum Link Model
• Review on novel methods for lattice gauge theories
• Optical Abelian Lattice Gauge Theories
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• U(1) Wilson lattice gauge theories in digital quantum simulators
• Confinement and lattice QED electric flux-tubes simulated with ultracold atoms
• General Methods for Digital Quantum Simulation of Gauge Theories
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Digital lattice gauge theories
• Quantum Algorithms for Simulating the Lattice Schwinger Model
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• SU(2) hadrons on a quantum computer
• Towards analog quantum simulations of lattice gauge theories with trapped ions
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Real Time Dynamics and Confinement in the ${\mathbb{Z}}_n$ Schwinger-Weyl lattice model for 1+1 QED
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Towards Quantum Simulating QCD
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Quantum simulation of lattice gauge theories using Wilson fermions
• Schwinger pair production with ultracold atoms
• Implementing quantum electrodynamics with ultracold atomic systems
• Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization
• Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory
• Reliability of lattice gauge theories
• Faster Digital Quantum Simulation by Symmetry Protection
• Oracles for Gauss's law on digital quantum computers
• Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Gluon Field Digitization via Group Space Decimation for Quantum Computers
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions
• Eliminating fermionic matter fields in lattice gauge theories
• Entanglement generation in $(1+1)D$ QED scattering processes
• Gauge protection in non-Abelian lattice gauge theories
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory
• SU(N) Irreducible Schwinger Bosons
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• Prepotential formulation of SU(3) lattice gauge theory
• Improved Hamiltonians for Quantum Simulations
• Quantum simulation of gauge theory via orbifold lattice
• Loop Approach to Lattice Gauge Theories
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Engineering a U(1) lattice gauge theory in classical electric circuits
• SU(2) Lattice Gauge Theory- Local Dynamics on Non-intersecting Electric flux Loops
• Irreducible SU(3) Schwinger Bosons
• Toward simulating Superstring/M-theory on a quantum computer
• Duality as a Feasible Physical Transformation

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