Towards quantum cellular automata with Rydberg atom arrays

A cellular automaton (CA) is a regular network of discrete variables that evolves based on local update rules. Even with such simple dynamics, CAs can exhibit complex behavior, the canonical example being the emergence of self-replicating patterns in Conway’s Game of Life. More recently, it was reported that classical CAs with non-thermal eigenstates can be used to probe non-ergodic quantum dynamics [1]. Quantum CAs extend such concepts to quantum systems and provide an alternate path to universal quantum computation and simulation. They are well-suited to studying lattice gauge theories, Floquet systems, and non-equilibrium physics [2]. Here, we present progress towards the first experimental demonstration of a quantum CA. Using a dual-species Rydberg atom array with global drives [3], we implement both classical and quantum CA update rules, and investigate the spread of entanglement in the system. Our work highlights the PXP model of the Rydberg atom array platform as a natural framework for implementing CAs.

[1] T. Iadecola and S. Vijay. Phys. Rev. B, 102(18), 180302 (2020).

[2] T. Farrelly. Quantum, 4, 368 (2020).

[3] S. Anand, C.E. Bradley, et al. Nature Physics, 20(11), 1744-1750 (2024).