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Coarse-grained quantum cellular automata

O. Duranthon
(
- LIS, Marseille and
- LPENS, Paris
)
,
Giuseppe Di Molfetta
(
- LIS, Marseille
)

Nov 9, 2020

8 pages

Published in:

Phys.Rev.A 103 (2021) 032224

Published: Mar 30, 2021

e-Print:

2011.04287 [quant-ph]

DOI:

10.1103/PhysRevA.103.032224

View in:

reference search6 citations

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Abstract: (arXiv)

One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size

N

; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes

N

of the cells. A byproduct of this simple toy-model is a general discrete analog of the Stokes law. Moreover we prove that in the spacetime limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qbits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.

Fundamental concepts
model: discrete
cellular automaton
space-time
field theory
superconductivity
Hamiltonian
resolution
toy model
ion

References(35)

Figures(13)

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