Simulating Lattice Gauge Theories within Quantum Technologies

Abstract

Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.

arXiv comment45 pages, 38 figures, review article

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• Dynamical localization transition in the non-Hermitian lattice gauge theory
• Many-Body Localization from Dynamical Gauge Fields
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Tunable photon-mediated interactions between spin-1 systems
• Ultrafast Hybrid Fermion-to-Qubit mapping
• Towards a Real-Time Computation of Timelike Hadronic Vacuum Polarization and Light-by-Light Scattering: Schwinger Model Tests
• The Coming Decades of Quantum Simulation
• Quantum State-Channel Duality for the calculation of Standard Model scattering amplitudes
• Quantum entropy couples matter with geometry
• State preparation of lattice field theories using quantum optimal control
• Real-time correlators in 3+1D thermal lattice gauge theory
• Stabilizer Scars
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Entanglement renormalization for gauge invariant quantum fields
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals
• Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Chiral fermion in the Hamiltonian lattice gauge theory
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Nonmesonic Quantum Many-Body Scars in a 1D Lattice Gauge Theory
• Time-Optimal Quantum Driving by Variational Circuit Learning
• Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Dynamical chirality production in one dimension
• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• A quantum information perspective on meson melting
• Steady-state Peierls transition in nanotube quantum simulator
• Exploring Many-body Interactions Through Quantum Fisher Information
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• From the Quantum Breakdown Model to the Lattice Gauge Theory
• Many-body localization regime for cavity induced long-range interacting models
• Phase diagram of 1+1D Abelian-Higgs model and its critical point
• Simulating Quantum Mechanics with a $\theta$-term and an 't Hooft Anomaly on a Synthetic Dimension
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Quantum walk of two anyons across a statistical boundary
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Spectral properties of critical 1+1D Abelian-Higgs model
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study
• Entanglement Properties of SU(2) Gauge Theory
• SU($N$) Toric Code and Nonabelian Anyons
• Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
• Observing quantum many-body scars in random quantum circuits
• Compressed quantum error mitigation
• Fractal states of the Schwinger model
• Quantum sampling for the Euclidean path integral of lattice gauge theory
• Lattice regularisation and entanglement structure of the Gross-Neveu model
• Field Tensor Network States
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
• Entanglement Witnessing for Lattice Gauge Theories
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• Triply-heavy/strange baryons with Cornell potential on a quantum computer
• Eight-dimensional topological systems simulated using time-space crystalline structures
• Towards Quantum Simulating Non-Abelian Gauge Theories
• Reflection and Transmission Amplitudes in a Digital Quantum Simulation
• Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories
• Tracking locality in time evolution of disordered systems
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• A single-particle framework for unitary lattice gauge theory in discrete time
• Symmetry-protected non-Abelian geometric phases in optical waveguides with nonorthogonal modes
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Quantum frustrated Wigner chains
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
• Cold atoms meet lattice gauge theory
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models
• Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Spectroscopy with the tensor renormalization group method
• Internal structure of gauge-invariant Projected Entangled Pair States
• Statistical Localization in a Rydberg Simulator of $U(1)$ Lattice Gauge Theory
• Inequality constraints in variational quantum circuits with qudits
• Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories
• Mass-Assisted Local Deconfinement in a Confined ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Quantum clustering and jet reconstruction at the LHC
• The Cytnx Library for Tensor Networks
• Simulating quantum field theories on gate-based quantum computers
• String breaking dynamics in Ising chain with local vibrations
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay
• Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
• Quantum Simulation of QED in Coulomb Gauge
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Lattice-enabled detection of spin-dependent three-body interactions
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Magic of discrete lattice gauge theories
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation
• Tuning long-range fermion-mediated interactions in cold-atom quantum simulators
• Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Universal quantum computation and quantum error correction with ultracold atomic mixtures
• Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD
• Partial confinement in a quantum-link simulator
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
• Engineering a Josephson junction chain for the simulation of the clock model
• Continuous-variable photonic quantum extreme learning machines for fast collider-data selection
• Quantum circuit for ${\mathbb{Z}}_3$ lattice gauge theory at nonzero baryon density
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Optical lattice quantum simulator of dynamics beyond Born-Oppenheimer
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Density-and-phase domain walls in a condensate with dynamical gauge potentials
• Benchmarking Digital-Analog Quantum Computation
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints
• Transverse Field $\gamma$-Matrix Spin Chains
• Quantum Monte Carlo and Stabilizer States
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Robust quantum many-body scars in lattice gauge theories
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d
• Relativistic meson spectra on ion-trap quantum simulators
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Localization Dynamics from Static and Mobile Impurities
• Real-space blocking of qubit variables on parallel lattice gauge theory links for quantum simulation
• Shearing approach to gauge-invariant Trotterization