Lattice gauge theories simulations in the quantum information era

Abstract

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analyzing the symmetry properties of Hamiltonian and states: the most striking example are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realization of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.

Pedagogical review article. Originally submitted to Contemporary Physics, the final version will appear soon on the on-line version of the journal. 34 pages

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• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Artificial gauge fields in materials and engineered systems
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
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• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
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• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Dynamical topological transitions in the massive Schwinger model with a θ-term
• 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
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• False vacuum decay in quantum spin chains
• Fermionic quantum processing with programmable neutral atom arrays
• Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization
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• Realizing a 1D topological gauge theory in an optically dressed BEC
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• Eliminating fermionic matter fields in lattice gauge theories
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• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
• Prethermalization in one-dimensional quantum many-body systems with confinement
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• Simulating 2D lattice gauge theories on a qudit quantum computer
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• Stabilizing lattice gauge theories through simplified local pseudo generators
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• Homogeneous Floquet time crystal protected by gauge invariance
• From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
• Scar States in Deconfined ${\mathbb{Z}}_2$ Lattice Gauge Theories
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
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• Molecular spin qudits for quantum simulation of light-matter interactions
• Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
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• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Enhancing disorder-free localization through dynamically emergent local symmetries
• Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator
• Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate
• Unruh effect for interacting particles with ultracold atoms
• Quantum Simulation of Chiral Phase Transitions
• Towards the continuum limit of a $(1+1)$d quantum link Schwinger model
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• Engineering a U(1) lattice gauge theory in classical electric circuits
• From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer
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• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
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• Periodically driven Rydberg chains with staggered detuning
• Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling
• Hidden order and symmetry protected topological states in quantum link ladders
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• A Cold-Atom Particle Collider
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories
• Synthetic Flux Attachment
• $Abinitio$ derivation of lattice gauge theory dynamics for cold gases in optical lattices
• Quantum simulator of link models using spinor dipolar ultracold atoms
• Detecting the critical point through entanglement in Schwinger model
• The mass of simple and higher-order networks
• Quantum Yang-Mills theory: an overview of a programme
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