Coarse-grained quantum cellular automata
arXiv:2011.04287 · doi:10.1103/PhysRevA.103.032224
Abstract
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 ; (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 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.
References in corpus (21)
- Reference frames, superselection rules, and quantum information
- Cellular automata approach to three-phase traffic theory
- A review of Quantum Cellular Automata
- Coarse-graining of cellular automata, emergence, and the predictability of complex systems
- Quantum Walks as simulators of neutrino oscillations in vacuum and matter
- Quantum walks and non-Abelian discrete gauge theory
- Coarse Grained Quantum Dynamics
- Quantum walks as massless Dirac Fermions in curved Space-Time
- Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
- The Dirac equation as a quantum walk over the honeycomb and triangular lattices
- A quantum cellular automaton for one-dimensional QED
- Quantum Walks, Weyl equation and the Lorentz group
- Emerging dynamics arising from coarse-grained quantum systems
- Quantum walks with a one-dimensional coin
- Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics
- Discrete-time quantum walks as fermions of lattice gauge theory
- Macro-to-micro quantum mapping and the emergence of nonlinearity
- Spin-entanglement wave in a coarse-grained optical lattice
- Virtually Abelian Quantum Walks
- Quantum-to-classical transition via quantum cellular automata
- Gauge-invariance in cellular automata
Cited by in corpus (7)
- Small-world complex network generation on a digital quantum processor
- Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
- Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics
- Geodesic Quantum Walks
- Renormalisation of Quantum Cellular Automata
- Entanglement dynamics and ergodicity breaking in a quantum cellular automaton
- Nonequilibrium phases and quantum correlations in synthetic transport models