Quantum walks and gravitational waves

Abstract

A new family of discrete-time quantum walks (DTQWs) propagating on a regular $(1+2)$D spacetime lattice is introduced. The continuous limit of these DTQWs is shown to coincide with the dynamics of a Dirac fermion interacting with an arbitrary relativistic gravitational field. This family is used to model the influence of arbitrary linear gravitational waves (GWs) on DTQWs. Pure shear GWs are studied in detail. On large spatial scales, pure shear GWs do not modify the polarizations of the fermion eigen-modes, but rescale all energies by a common factor. On smaller scales typically comparable to two or three lattice steps, both polarizations and energies are modified in a non-trivial way. This effect is particularly salient on interference patterns between the fermion eigen-modes.

11 pages, 4 figures

References in corpus (5)

• 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
• Quantum walks and non-Abelian discrete gauge theory
• Quantum State Transfer in Spin-1 Chains

Cited by in corpus (17)

• A quantum cellular automaton for one-dimensional QED
• The Dirac equation as a quantum walk over the honeycomb and triangular lattices
• Simulating Dirac Hamiltonian in Curved Space-time by Split-step Quantum Walk
• Quantum walks in weak electric fields and Bloch oscillations
• From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
• Dirac quantum walks on triangular and honeycomb lattices
• Action Principles for Quantum Automata and Lorentz Invariance of Discrete Time Quantum Walks
• Discrete-time quantum walks as fermions of lattice gauge theory
• Quantum simulation of quantum relativistic diffusion via quantum walks
• A single-particle framework for unitary lattice gauge theory in discrete time
• A quantum walk simulation of extra dimensions with warped geometry
• Clifford algebra from quantum automata and unitary Wilson fermions
• Quantum Simulation of a Discrete-Time Quantum Stochastic Walk
• Quantum Simulation of Neutrino Oscillation and Dirac Particle Dynamics in Curved Space-time
• Geodesic Quantum Walks
• Simulating Non Commutative Geometry with Quantum Walks
• Discrete Geometry from Quantum Walks