A single-particle framework for unitary lattice gauge theory in discrete time
arXiv:2208.14997 · doi:10.1088/1367-2630/acac47
Abstract
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations.
References in corpus (15)
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Optical Abelian Lattice Gauge Theories
- Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
- Reversible quantum cellular automata
- Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
- Quantum Algorithms for Fermionic Quantum Field Theories
- Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
- Quantum cellular automata and free quantum field theory
- Towards overcoming the Monte Carlo sign problem with tensor networks
- Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
- Quantum lattice gas algorithmic representation of gauge field theory
- Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
- The Hadron Spectrum from Lattice QCD
- Exponential tail estimates for quantum lattice dynamics
- Clifford algebra from quantum automata and unitary Wilson fermions