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

Samuel Loomis and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

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.


Samuel Loomis and James P. Crutchfield, “Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes”, 176:6 (2018) 1317-1342.
doi:10.1007/s10955-019-02344-x.
[pdf]

arxiv.org:1808.08639.