Iterative model of self-referential quantum evolution

Abstract: We introduce and analyze a toy model of a quantum physical device capable of internal, self-referential deliberation, realized through iterative, branch-dependent unitary evolution tracked by control, memory, and policy registers. The key idea is to represent ``deliberation'' as a coherent branching process, in which alternative candidate evolutions are maintained in superposition across registers, rather than by placing the system itself under a literal superposition of Hamiltonians. We provide explicit quantum circuit realizations, carry through detailed step-by-step derivations of the entangled memory--policy dynamics, and analyze the constraints imposed by the no-cloning theorem on coherent information flow. We also briefly discuss categorical reformulations and their conceptual implications. Taken together, this frames the model as a plausible setting for exploring how such devices may maintain multiple alternatives in parallel, providing a formal framework for investigating internally coherent decision processes through coherent branching, entanglement, and self-modifying unitary dynamics.