• Corpus ID: 235293860

Reversible Cellular Automata as Integrable Interactions Round-a-Face: Deterministic, Stochastic, and Quantized

  title={Reversible Cellular Automata as Integrable Interactions Round-a-Face: Deterministic, Stochastic, and Quantized},
  author={Toma{\vz} Prosen},
  • T. Prosen
  • Published 2 June 2021
  • Physics, Mathematics
A family of reversible deterministic cellular automata, including the rules 54 and 201 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] as well as their kinetically constrained quantum (unitary) or stochastic deformations, is shown to correspond to integrable Floquet circuit models with local interactions round-a-face. Using inhomogeneous solutions of the star-triangle relation with a one or two dimensional spectral parameter, changing their functional form depending on the orientation… 

Figures from this paper

Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations. We show that such


Exact matrix product decay modes of a boundary driven cellular automaton
We study integrability properties of a reversible deterministic cellular automaton (the rule 54 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]) and present a bulk algebraic relation and its
Integrability of a deterministic cellular automaton driven by stochastic boundaries
We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158,
Time-Dependent Matrix Product Ansatz for Interacting Reversible Dynamics
We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the
A review of Quantum Cellular Automata
This review discusses all of these applications of QCAs, including the matrix product unitary approach and higher dimensional classifications, as well as some other interesting results on the structure of quantum cellular automata.
Facilitated quantum cellular automata as simple models with non-thermal eigenstates and dynamics
We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so
Integrable Many-Body Quantum Floquet-Thouless Pumps.
An interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion that exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.
On two integrable cellular automata
We describe two simple cellular automata (CA) models which exhibit the essential attributes of soliton systems. The first one is an invertible, 2-state, 1-dimensional CA or, in other words, a
Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
The box–ball system is an integrable cellular automaton on a one-dimensional lattice. It arises from either quantum or classical integrable systems by procedures called crystallization and
Operator growth and eigenstate entanglement in an interacting integrable Floquet system
We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model. We argue that this model is integrable, with a quasiparticle
Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states.