From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer
arXiv:2006.01258 · doi:10.1088/1367-2630/abb961
Abstract
The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of Abelian gauge theories, the quantum simulation of non-Abelian gauge theories appears still elusive. In this paper we present minimal non-Abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.
References in corpus (58)
- Anyons in an exactly solved model and beyond
- Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- A spin-orbit coupled Bose-Einstein condensate
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Light-induced gauge fields for ultracold atoms
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
- Scalable Quantum Simulation of Molecular Energies
- 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
- 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 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
- Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
- Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter
- Lattice gauge theories and string dynamics in Rydberg atom quantum simulators
- A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
- Lattice gauge theories simulations in the quantum information era
- Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
- Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
- Simulations of non-Abelian gauge theories with optical lattices
- The mass spectrum of the Schwinger model with Matrix Product States
- 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
- Optical Abelian Lattice Gauge Theories
- Photons and electrons as emergent phenomena
- Confinement and lattice QED electric flux-tubes simulated with ultracold atoms
- Quantum simulation of a lattice Schwinger model in a chain of trapped ions
- Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory
- Digital lattice gauge theories
- Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
- Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields
- Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
- Digital quantum simulation of lattice gauge theories with dynamical fermionic matter
- Non-Abelian Lattice Gauge Theories in Superconducting Circuits
- Gauge-invariant implementation of the Abelian Higgs model on optical lattices
- Digital quantum simulation of lattice gauge theories in three spatial dimensions
- Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
- Quantum simulation of the universal features of the Polyakov loop
- Schwinger pair production with ultracold atoms
- Quantum simulation of lattice gauge theories using Wilson fermions
- Implementing quantum electrodynamics with ultracold atomic systems
- Oracles for Gauss's law on digital quantum computers
- Discrete Abelian Gauge Theories for Quantum Simulations of QED
- Fermion production from real-time lattice gauge theory in the classical-statistical regime
- Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms
- Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
- Toolbox for Abelian lattice gauge theories with synthetic matter
- SO(3) "Nuclear Physics" with ultracold Gases
- CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices
- gauge theories coupled to topological fermions: QED with a quantum-mechanical angle
- Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons
- Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators
- Back-reaction in strong field QED: a toy model
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- Advances in QED with intense background fields
- Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
- SU(2) hadrons on a quantum computer
- Quantum Simulating Nature's Fundamental Fields
- A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
- Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
- SU(2) lattice gauge theory on a quantum annealer
- Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer
- Single-particle digitization strategy for quantum computation of a scalar field theory
- Thermalization of Gauge Theories from their Entanglement Spectrum
- From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
- Scalable cold-atom quantum simulator for two-dimensional QED
- Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate
- Observing dynamical currents in a non-Hermitian momentum lattice
- Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer
- Engineering a U(1) lattice gauge theory in classical electric circuits
- Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
- From square plaquettes to triamond lattices for SU(2) gauge theory
- Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
- Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities
- Quantum Simulation of the N flavor Gross-Neveu Model
- Scalable, ab initio protocol for quantum simulating SU()U(1) Lattice Gauge Theories
- Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
- Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to
- Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
- Revisiting the Jaynes-Cummings model with time-dependent coupling
- Cold atoms meet lattice gauge theory