Quantum Cellular Automata on a Rydberg Atom-Array

Neutral atom arrays have recently scaled up to 1000s of physical qubits, but still face the challenge of large-scale individual qubit control to successfully implement the circuit model of quantum computing. An alternative paradigm, quantum cellular automata (QCAs) offer near-term opportunities to explore digital quantum simulation. QCAs are a class of systems that require only global control operations applied on a suitable initial state with local update constraints. In this talk, I will describe our recent work on implementing multiple QCAs on a one-dimensional chain of interleaved rubidium (Rb) and cesium (Cs) atoms. The first automaton we explore is based on a Floquet-PXP model. Under this evolution, we show quasiparticle dynamics through interacting domain walls, and exploit this to prepare GHZ-states on up to 5-atoms. Next, we introduce a graph-state automaton, using Rb to mediate entangling gates on Cs. Using this gate, we demostrate parallel preparation of high-fidelity Bell-states on Cs. We then implement this sequence on a larger chain to prepare a 17-qubit cluster-state, in which we verify bi-partite entanglement. Finally, we repeatedly apply this operation on chains of 5 Cs + 4 Rb atoms, and track the time-evolution of Pauli strings. Some of these operators behave as gliders, and travel without dispersion across the chain. Our work thus highlights the natural application of dual-element atom arrays in implementing QCAs.