On the challenges of using D-Wave computers to sample Boltzmann Random Variables

Pochart, Thomas; Jacquot, Paulin; Mikael, Joseph

doi:10.48550/arxiv.2111.15295

Cited by 1 publication

(3 citation statements)

References 10 publications

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“…In this section we touch on some of these difficulties and discuss some possible methods to mitigate them. Around the time this thesis was started, Pochart et al released a paper [37] in which they discuss challenges associated with using a D-Wave annealer to sample Boltzmann random variables.…”

Section: Challenges Of Using a D-wave Annealer To Train Qbmsmentioning

confidence: 99%

“…It is natural to think that one could just combine the results from multiple sample sets, but this is not necessarily the case. Due to the spin-bath polarization effect (see error sources below), one cannot combine sample sets because of the possibility of previous samples affecting future ones [37].…”

Section: Maximum Sample Set Sizementioning

confidence: 99%

“…Due to the limited maximum sample size of 10 4 when using a D-Wave annealer and the inability to concatenate sample sets due to spin-bath polarization effects [37], it makes computation of the KL divergence quite difficult because we cannot get a proper read on the probability distribution when the number of possible states is high. Even for the small 12-qubit problem there are still 2 12 = 4096 possible states, thus 10 4 samples are not entirely representative of the true distribution.…”

Section: Appendix Amentioning

confidence: 99%

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Quantum Boltzmann Machines: Applications in Quantitative Finance

Perot¹

2023

Preprint

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In this thesis we explore using the D-Wave Advantage 4.1 quantum annealer to sample from quantum Boltzmann distributions and train quantum Boltzmann machines (QBMs). We focus on the real-world problem of using QBMs as generative models to produce synthetic foreign exchange market data and analyze how the results stack up against classical models based on restricted Boltzmann machines (RBMs). Additionally, we study a small 12-qubit problem which we use to compare samples obtained from the Advantage 4.1 with theory, and in the process gain vital insights into how well the Advantage 4.1 can sample quantum Boltzmann random variables and be used to train QBMs. Through this, we are able to show that the Advantage 4.1 can sample classical Boltzmann random variables to some extent, but is limited in its ability to sample from quantum Boltzmann distributions. Our findings indicate that QBMs trained using the Advantage 4.1 are much noisier than those trained using simulations and struggle to perform at the same level as classical RBMs. However, there is the potential for QBMs to outperform classical RBMs if future generation annealers can generate samples closer to the desired theoretical distributions.

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Section: Challenges Of Using a D-wave Annealer To Train Qbmsmentioning

confidence: 99%

Section: Maximum Sample Set Sizementioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

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