Memory compression and thermal efficiency of quantum implementations of nondeterministic hidden Markov models

Abstract

Stochastic modeling is an essential component of the quantitative sciences, with hidden Markov models (HMMs) often playing a central role. Concurrently, the rise of quantum technologies promises a host of advantages in computational problems, typically in terms of the scaling of requisite resources such as time and memory. HMMs are no exception to this, with recent results highlighting quantum implementations of deterministic HMMs exhibiting superior memory and thermal efficiency relative to their classical counterparts. In many contexts, however, nondeterministic HMMs are viable alternatives; compared to them, the advantages of current quantum implementations do not always hold. Here, we provide a systematic prescription for constructing quantum implementations of nondeterministic HMMs that reestablish the quantum advantages against this broader class. Crucially, we show that whenever the classical implementation suffers from thermal dissipation due to its need to process information in a time-local manner, our quantum implementations will both mitigate some of this dissipation and achieve an advantage in memory compression.

Standardized Evaluation Method of Pronunciation Teaching Based on Deep Learning

“…In addition, several CALL systems at home and abroad primarily focus on the learning of vocabulary and grammar because of the limitations of technology. Only one or two assessment indications are used as the foundation for evaluation, and there are functional problems that can only offer students an overall score [8]. Despite this, the traditional evaluation of pronunciation in oral language teaching still relies on manual scoring with considerable subjective willingness, diverse criteria, and a slow pace.…”

Implementing quantum dimensionality reduction for non-Markovian stochastic simulation

“…Quantum models of stochastic processes have also been shown to exhibit other advantages over classical models that can be explored, such as reduced thermal dissipation 20 , 21 . We also note a close connection with studies on the fundamental limits of classical and quantum clocks 22 – 24 , the latter of which have been shown to exhibit memory/accuracy advantages.…”

Thermodynamics of deterministic finite automata operating locally and periodically

“…Finally, it is interesting to consider how the consequences of locality and periodicity relate to other resource costs. Recent work on transducers-a computational machine that generates an output corresponding to a hidden Markov model-has shown that a quantum advantage exists over a classical implementation if and only if the machine is not locally invertible [40]; it is unclear whether a similar result holds for DFA. The role of the input distribution in determining the thermodynamic costs in our work is also reminiscent of the way computational complexity depends on the distribution over inputs.…”