A quantum walk with both a continuous-time and a continuous-spacetime limit
Abstract
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a Quantum Walks or Quantum Cellular Automata-based) enjoying a relativistic continuous spacetime limit. We provide a first example of a quantum simulation scheme that unifies both approaches. The proposed scheme supports both a continuous-time discrete-space limit, leading to lattice fermions, and a continuous-spacetime limit, leading to the Dirac equation. The transition between the two can be thought of as a general relativistic change of coordinates, pushed to an extreme. As an emergent by-product of this procedure, we obtain a Hamiltonian for lattice-fermions in curved spacetime with synchronous coordinates.
Cite
@article{arxiv.1906.04483,
title = {A quantum walk with both a continuous-time and a continuous-spacetime limit},
author = {Giuseppe Di Molfetta and Pablo Arrighi},
journal= {arXiv preprint arXiv:1906.04483},
year = {2019}
}