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Sequential growth dynamics and quantum random walks

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Rideout and Sorkin proposed a classical dynamics for causal sets based upon a sequential growth model. Comparing it with models for sequential growth in other systems, and with the dual goals of generating manifold-like causal sets and finding a quantum dynamics for them, we propose some modifications to their model. The resulting, admittedly speculative, proposal is a type of quantum random walk. We explore its properties in some simple cases.