A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations

Abstract

We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating frame, where the matter is decoupled from the gauge constraints, we can express the gauge field operators in terms of dual operators. In two space dimensions, the dual representation is completely free of any local constraints. In three space dimensions, local constraints among the dual operators remain but involve only the gauge field degrees of freedom (and not the matter degrees of freedom). These formulations, which reduce the required Hilbert space dimension, could be useful for both numerical (classical) Hamiltonian computations and quantum simulation or computation.

arXiv comment16 pages, 5 figures, v2: as published

References in corpus (32)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The phase diagram of dense QCD
• Simulating Lattice Gauge Theories within Quantum Technologies
• 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
• Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator
• Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter
• Lattice gauge theories simulations in the quantum information era
• Simulations of non-Abelian gauge theories with optical lattices
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• QCD as a Quantum Link Model
• Review on novel methods for lattice gauge theories
• Optical Abelian Lattice Gauge Theories
• Digital lattice gauge theories
• Analog quantum chemistry simulation
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• The Bond-Algebraic Approach to Dualities
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory
• 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
• Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory
• Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states
• Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

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• Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
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• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Duality as a Feasible Physical Transformation
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Towards the real-time evolution of gauge-invariant ${\mathbb{Z}}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation
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• 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
• An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension
• Quantum Computing for Energy Correlators
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• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
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• Dynamics of quarks and gauge fields in the lowest-energy states in QCD and QED
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• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Encoding a topological gauge theory on a ring-shaped Raman-coupled Bose gas
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• Shearing approach to gauge-invariant Trotterization
• Mean Field Approaches to Lattice Gauge Theories: A Review