Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2010.14135 · Physics Letters A

Group theory on quantum Boltzmann machine

Hai-Jing Song, D. L. Zhou

Published Mar 19, 2021• 4 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2021.127298

Related papers

Quantum Boltzmann Machine

Bohdan Kulchytskyy, Evgeny Andriyash, Mohammed Amin +1 more

Bulletin of the American Physical Society•Mar 18, 2016•21 citations

Quantum Thermodynamics of Quantum Boltzmann Machines

Sangchul Oh, Sabre Kais

Bulletin of the American Physical Society•Mar 18, 2021•0 citations

Quantum Boltzmann Machine and Thermofield Dynamics

Vinícius N. A. Lula-Rocha, Marco A. S. Trindade, J. D. M. Vianna

Brazilian Journal of Physics•Apr 26, 2023•1 citation

Improved Training of Quantum Boltzmann Machines

Eric R. Anschuetz, Yudong Cao

Bulletin of the American Physical Society•Mar 5, 2019•0 citations

Quantum Boltzmann Machines: Applications in Quantitative Finance

Cameron Perot

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.

arXiv:2301.13295•Jan 30, 2023•0 citations

Quantum Boltzmann machines: Clifford algebras and asymptotic analysis

Marco A. S. Trindade, Vinícius N. A. Lula-Rocha

Abstract We analyze mathematical aspects related to general quantum Boltzmann machine models through representations of algebras and functional analytic techniques. In this context, based on algebraic formulation we show the existence of a symmetry group for a class of Hamiltonians based on generators of Clifford algebras and discuss its implications for the learning scheme. Also, we have developed a rigorous mathematical analysis that allows us to investigate issues related to the asymptotic behavior of quantum Boltzmann machines. Particularly, we obtain a lower bound of fidelity in terms of the upper limit of quantum relative entropy.

Physica Scripta•May 31, 2024•1 citation
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.
Abstract We analyze mathematical aspects related to general quantum Boltzmann machine models through representations of algebras and functional analytic techniques. In this context, based on algebraic formulation we show the existence of a symmetry group for a class of Hamiltonians based on generators of Clifford algebras and discuss its implications for the learning scheme. Also, we have developed a rigorous mathematical analysis that allows us to investigate issues related to the asymptotic behavior of quantum Boltzmann machines. Particularly, we obtain a lower bound of fidelity in terms of the upper limit of quantum relative entropy.