A quantum walk with both a continuous-time limit and a continuous-spacetime limit

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 rela...

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Bibliographic Details
Published in:Quantum information processing 2020-02, Vol.19 (2), Article 47
Main Authors: Di Molfetta, Giuseppe, Arrighi, Pablo
Format: Article
Language:English
Subjects:
Cellular automata
Computer simulation
Data Structures and Information Theory
Dirac equation
Fermions
Flavor (particle physics)
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum mechanics
Quantum Physics
Relativism
Relativistic effects
Spacetime
Spintronics
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-019-2549-2