Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection

Abstract

Recent advancements in the field of quantum simulation have significantly expanded the potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a central challenge, especially for large-scale non-Abelian LGTs with dynamical matter, which are particularly complex in terms of engineering for experiments. Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs) and controlling the magnitude of its effect is an open challenge. Here, we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature. Second, we present a proposal for a novel gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian $U(2)$ LGTs with dynamical fermionic matter in $(2+1)$ dimensions on large scales. Due to the simplicity of the gauge protection mechanism, based on a Zeeman shift in combination with superexchange interactions, our scheme can be naturally included in other rishon-based quantum simulation protocols. Third, we extend our approach to a fully scalable, hybrid digital-analog simulator for $U(N)$ LGTs based on Rydberg AELA with variable rishon number. The proposed general mechanism for gauge protection provides a promising path towards the long-awaited simulation of non-Abelian LGTs relevant to particle physics.

References in corpus (48)

• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Quantum Simulation for High Energy Physics
• 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
• Thermalization dynamics of a gauge theory on a quantum simulator
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Direct observation of coherent inter-orbital spin-exchange dynamics
• Observation of many-body scarring in a Bose--Hubbard quantum simulator
• Dissipation induced Tonks-Girardeau gas in an optical lattice
• Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
• SU(2) hadrons on a quantum computer
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Gauge protection in non-Abelian lattice gauge theories
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Simulating 2D lattice gauge theories on a qudit quantum computer
• Stabilizing lattice gauge theories through simplified local pseudo generators
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Probing confinement in a ${\mathbb{Z}}_2$ lattice gauge theory on a quantum computer
• Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator
• Probing transport and slow relaxation in the mass-imbalanced Fermi-Hubbard model
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Observation of string breaking on a (2 + 1)D Rydberg quantum simulator
• Manipulating synthetic gauge fluxes via multicolor dressing of Rydberg-atom arrays
• Floquet-Tailored Rydberg Interactions
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
• Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles
• Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• $Abinitio$ derivation of lattice gauge theory dynamics for cold gases in optical lattices
• Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density
• Quantum Simulation of Lattice Gauge Theories on Superconducting Circuits: Quantum Phase Transition and Quench Dynamics
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Transitionless quantum driving in spin echo
• Magic running- and standing-wave optical traps for Rydberg atoms
• Simulation of chiral motion of excitation within the ground-state manifolds of neutral atoms