Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
arXiv:1404.4499 · doi:10.1088/1367-2630/16/9/093007
Abstract
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the first-order-only covariance of the Dirac QW. We then introduce the Clock QW and the Clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.
arXiv comment21 pages, 15 figures
References in corpus (18)
- Quantum Information and Relativity Theory
- From quantum cellular automata to quantum lattice gases
- Lattice Boltzmann Equation for Quantum Mechanics
- Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
- Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
- Quantum Picturalism
- Index theory of one dimensional quantum walks and cellular automata
- Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
- Reversible quantum cellular automata
- Quantum Walks in artificial electric and gravitational Fields
- Discrete-time quantum walks: continuous limit and symmetries
- Action principle for cellular automata and the linearity of quantum mechanics
- Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
- Discrete Spacetime and Relativistic Quantum Particles
- The Dirac Quantum Cellular Automaton in one dimension: Zitterbewegung and scattering from potential
- Relativistic effects in quantum walks: Klein's paradox and Zitterbewegung
- Decoupled Quantum Walks, models of the Klein-Gordon and wave equations
- Duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions
Cited by in corpus (33)
- A review of Quantum Cellular Automata
- A quantum cellular automaton for one-dimensional QED
- The Dirac equation as a quantum walk over the honeycomb and triangular lattices
- Quantum Causal Graph Dynamics
- Quantum Walks, Weyl equation and the Lorentz group
- Solutions of a two-particle interacting quantum walk
- Quantum walks with a one-dimensional coin
- Discrete spacetime, quantum walks and relativistic wave equations
- From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
- Action Principles for Quantum Automata and Lorentz Invariance of Discrete Time Quantum Walks
- Isotropic quantum walks on lattices and the Weyl equation
- Detection of discrete spacetime by matter interferometry
- A relativistic discrete spacetime formulation of 3+1 QED
- Discrete-time quantum walks as fermions of lattice gauge theory
- Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
- A gauge-invariant reversible cellular automaton
- Coarse-grained quantum cellular automata
- Twisted quantum walks, generalised Dirac equation and Fermion doubling
- Simple derivation of the Weyl and Dirac quantum cellular automata
- Quantum simulation of quantum relativistic diffusion via quantum walks
- Chirality from quantum walks without quantum coin
- Dynamical Triangulation Induced by Quantum Walk
- A single-particle framework for unitary lattice gauge theory in discrete time
- Symmetries of the Dirac quantum walk and emergence of the de Sitter group
- Quantum State Transfer through Noisy Quantum Cellular Automata
- A perturbative approach to the solution of the Thirring quantum cellular automaton
- Gauge-invariance in cellular automata
- Landau levels for discrete-time quantum walks in artificial magnetic fields
- Renormalisation of Quantum Cellular Automata
- Simulating Non Commutative Geometry with Quantum Walks
- Local Probability Conservation in Discrete Time Quantum Walks
- Reversibility in one-dimensional quantum cellular automata in the presence of noise
- Quantum Coherence in Noisy Cellular Automata