Quantum walks and gravitational waves

TL;DR

This paper introduces a new class of discrete-time quantum walks that simulate Dirac fermions in curved spacetime, specifically modeling how gravitational waves influence quantum states and interference patterns.

Contribution

It develops a family of quantum walks whose continuous limit matches Dirac fermions in gravitational fields, enabling simulation of gravitational wave effects on quantum systems.

Findings

Pure shear GWs rescale fermion energies without changing polarizations on large scales.

On small scales, GWs modify both energies and polarizations non-trivially.

Interference patterns between fermion modes are significantly affected by GWs.

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.