Quantum hidden Markov models based on transition operation matrices

Cholewa, Michał; Gawron, Piotr; Głomb, Przemysław; Kurzyk, Dariusz

doi:10.1007/s11128-017-1544-8

Cited by 13 publications

(4 citation statements)

References 18 publications

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“…In the context of the causal discovery, we impose a Markov property on the graph. Quantum mechanics involves difficult issues regarding state transitions, and there exists the notion of a quantum Markov process Barry et al (2014); Cholewa et al (2017); Monras et al (2010). Causal discovery is one useful application that has been successful using graphical models, but it can be extended quantum mechanically.…”

Section: Application To Machine Learning and Causal Discoverymentioning

confidence: 99%

Estimation of mutual information via quantum kernel methods

Maeda,

Tezuka,

Kawaguchi

2024

Preprint

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Recently, the importance of analyzing data and collecting valuable insight efficiently has been increasing in various fields. Estimating mutual information~(MI) plays a critical role in investigating the relationship among multiple random variables with a nonlinear correlation. Particularly, the task to determine whether they are independent or not is called the independence test, whose core subroutine is estimating MI from given data. It is a fundamental tool in statistics and data analysis that can be applied in a wide range of applications such as hypothesis testing, causal discovery and more. In this paper, we propose a method for estimating mutual information using the quantum kernel. We investigate the performance under various problem settings, such as different sample sizes or the shape of the probability distribution. As a result, the quantum kernel method showed higher performance than the classical one under the situation that the number of samples is small, the variance is large or the variables possess highly non-linear relationships. We discuss this behavior in terms of the central limit theorem and the structure of the corresponding quantum reproducing kernel Hilbert space.

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Section: Application To Machine Learning and Causal Discoverymentioning

confidence: 99%

Estimation of mutual information via quantum kernel methods

Maeda,

Tezuka,

Kawaguchi

2024

Preprint

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“…Technologies based on this paradigm offer a means to implement better, faster, more efficient algorithms and protocols [15]. Naturally, this has spurred investigations into quantum extensions of HMMs, including characterization of their expressivity [16][17][18][19][20][21], how they can be inferred [22][23][24], and how they can outperform classical automata [25,26].…”

Section: Introductionmentioning

confidence: 99%

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

Elliott

2021

Phys. Rev. A

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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.

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“…Technologies based on this paradigm offer a means to implement better, faster, more efficient algorithms and protocols [15]. Naturally, this has spurred investigations into quantum extensions of HMMs, including characterisation of their expressivity [16][17][18][19][20][21], how they can be inferred [22][23][24], and how they can outperform classical automata [25,26].…”

Section: Introductionmentioning

confidence: 99%

Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models

Elliott

2021

Preprint

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Quantum hidden Markov models based on transition operation matrices

Cited by 13 publications

References 18 publications

Estimation of mutual information via quantum kernel methods

Estimation of mutual information via quantum kernel methods

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

Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models

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