We propose a physical platform for quantum information processing that is inherently parallelisable, does not require individual addressing and takes full advantage of both unitary and non-unitary multiqubit interactions. The key innovation is the use of programmable multifrequency excitation and depumping of Rydberg states that provides a natural implementation of the so-called quantum cellular automata (QCA) paradigm. We show that this leads to a rich diversity of controllable quantum dynamics in both discrete and continuous time evolution. We also numerically demonstrate that QCA is well-suited for variational optimisation, a hybrid quantum-classical feedback loop that is capable of steering the open quantum dynamics towards highly entangled GHZ states. The generation of such highly entangled states can serve as an valuable resource for quantum sensing and quantum information processing. Our proposed QCA implementation provides a novel and physically viable approach to quantum information processing that is uniquely adapted to the strengths of the Rydberg atom platform.