Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes

Samuel Loomis; James P. Crutchfield

doi:10.1007/s10955-019-02344-x

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arXiv · 1808.08639

Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes

Samuel Loomis·James P. Crutchfield

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Abstract

Among the predictive hidden Markov models that describe a given stochastic process, the ε-machine is strongly minimal in that it minimizes every Rényi-based memory measure. Quantum models can be smaller still. In contrast with the ε-machine's unique role in the classical setting, however, among the class of processes described by pure-state hidden quantum Markov models, there are those for which there does not exist any strongly minimal model. Quantum memory optimization then depends on which memory measure best matches a given problem circumstance.

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BibTeX RIS

Samuel Loomis, James P. Crutchfield. 2018-08-26. Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes. https://doi.org/10.1007/s10955-019-02344-x

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