Discrete-time quantum walks: continuous limit and symmetries
arXiv:1111.2165 · doi:10.1063/1.4764876
Abstract
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks do. All families (1-jets) admitting a continuous limit are identified. The continuous limit is described by a Dirac-like equation or, alternately, a couple of Klein-Gordon equations. Variational principles leading to these equations are also discussed, together with local invariance properties.
References in corpus (8)
- Quantum walks of correlated particles
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- Relativistic Brownian Motion
- Connecting the discrete and continuous-time quantum walks
- Relationship Between Quantum Walk and Relativistic Quantum Mechanics
- Quantum State Transfer in Spin-1 Chains
Cited by in corpus (32)
- Quantum walks: a comprehensive review
- A review of Quantum Cellular Automata
- Quantum Walks in artificial electric and gravitational Fields
- Quantum Field as a quantum cellular automaton: the Dirac free evolution in one dimension
- Quantum Walks as simulators of neutrino oscillations in vacuum and matter
- Quantum Walks and discrete Gauge Theories
- Quantum walks and non-Abelian discrete gauge theory
- Quantum walks as massless Dirac Fermions in curved Space-Time
- Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
- Discrete-time quantum walk with feed-forward quantum coin
- Quantum Lattice Boltzmann is a quantum walk
- Dirac Quantum Cellular Automaton from Split-step Quantum Walk
- Quantum walks and gravitational waves
- Algorithm for the solution of the Dirac equation on digital quantum computers
- Simulating Dirac Hamiltonian in Curved Space-time by Split-step Quantum Walk
- Decoupled Quantum Walks, models of the Klein-Gordon and wave equations
- From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
- Continuous Limit of Discrete Quantum Walks
- Continuous limits of linear and nonlinear quantum walks
- A relativistic discrete spacetime formulation of 3+1 QED
- Quantum walk on a cylinder
- Edge states in a two-dimensional quantum walk with disorder
- Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
- Entanglement dynamics and phase transitions of the Floquet cluster spin chain
- Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
- Twisted quantum walks, generalised Dirac equation and Fermion doubling
- Quantum walk on a graph of spins: magnetism and entanglement
- Landau levels for discrete-time quantum walks in artificial magnetic fields
- An overview of Quantum Cellular Automata
- Scattering and inverse scattering for nonlinear quantum walks
- Exact simulation of coined quantum walks with the continuous-time model
- Kinematics and Dynamics of Quantum Walks in terms of Systems of Imprimitivity