2024/06/07 by Wout Merbis, Merbis, Wout, Calvin Bakker +1 · 1 citation
Computer Science · Physics and Astronomy · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2406.04895
openalex publication_date 2024/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into Wolfram's complexity classes. Here, we propose a quantitative measure, rooted in quantum information theory, to categorize the complexity of classical deterministic cellular automata. Specifically, we construct a Matrix Product Operator (MPO) of the transition matrix on the space of all possible CA configurations. We find that the growth of entropy of the singular value spectrum of the MPO reveals the complexity of the CA and can be used to characterize its dynamical behavior. This measure defines the concept of operator entanglement entropy for CA, demonstrating that quantum information measures can be meaningfully applied to classical deterministic systems.