Computation in Finitary Quantum Processes

We introduce quantum finite-state generators as a first step toward completing a computational description of observing individual quantum systems over time. We develop the mathematical foundations of quantum finite-state machines and compare nondeterministic and deterministic versions to stochastic generators and recognizers, summarizing their relative computational power via a hierarchy of finitary process languages. Quantum finite-state generators are explored via several physical examples, including the iterated beam splitter, the quantum kicked top, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that the behavior of these systems, and so their information processing capacity, depends sensitively on measurement protocol.

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