Computation in Finitary Stochastic and Quantum Processes [article]

Karoline Wiesner, James P. Crutchfield
2008 arXiv   pre-print
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and
more » ... tors are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated beam splitter, an atom in a magnetic field, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that these systems' behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.
arXiv:quant-ph/0608206v4 fatcat:rjkyslchxrakrfybdg4ie7lglm