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Article Dans Une Revue Physical Review A Année : 2021

Coarse-grained quantum cellular automata

Résumé

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.
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Dates et versions

hal-03034747 , version 1 (07-09-2023)

Identifiants

Citer

O. Duranthon, Giuseppe Di Molfetta. Coarse-grained quantum cellular automata. Physical Review A, 2021, 103, pp.032224. ⟨10.1103/PhysRevA.103.032224⟩. ⟨hal-03034747⟩
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