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

Understand

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.