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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-02165580
Contributor : Inspire Hep <>
Submitted on : Wednesday, June 26, 2019 - 9:06:05 AM
Last modification on : Wednesday, February 12, 2020 - 2:06:48 AM

Links full text

Identifiers

Citation

Giuseppe Di Molfetta, Pablo Arrighi. A quantum walk with both a continuous-time and a continuous-spacetime limit. 2019. ⟨hal-02165580⟩

Share

Metrics

Record views

50