A quantum cellular automaton for one-dimensional QED
arXiv:1903.07007 · doi:10.1007/s11128-019-2555-4
Abstract
We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a "convergent" sequence of quantum cellular automata, parameterized by the spacetime lattice spacing---encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics.
15 pages, 4 figures, v2: typo corrected
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- A relativistic discrete spacetime formulation of 3+1 QED
- Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
- Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions
- Scattering and perturbation theory for discrete-time dynamics
- Coarse-grained quantum cellular automata
- Quantum cellular automata for quantum error correction and density classification
- Holographic networks for (1+1)-dimensional de Sitter spacetime
- Non-Abelian Gauge-Invariant Cellular Automata
- Discretizing quantum field theories for quantum simulation
- A single-particle framework for unitary lattice gauge theory in discrete time
- Quantum Electrodynamics from Quantum Cellular Automata, and the Tension Between Symmetry, Locality and Positive Energy
- Gauge-invariance in cellular automata
- A perturbative approach to the solution of the Thirring quantum cellular automaton
- On quantum superpositions of graphs, no-signalling and covariance
- The Dirac Vacuum in Discrete Spacetime
- Renormalisation of Quantum Cellular Automata
- Feynman checkers: lattice quantum field theory with real time
- Bounds on QCA Lattice Spacing from Data on Lorentz Violation
- Fermion Doubling in Dirac Quantum Walks
- Recurrence Time for Finite Quantum Systems