mlsanityData to 7 Oct 2026

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines

arXiv 1712.04144 ↗First posted 12 Dec 2017physics.data-an cond-mat.stat-mech quant-phcited by 33

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Abstract (arXiv)

We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states respectively.Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the restricted Boltzmann machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches. We verify our reasonings by comparing the performance of RBMs of various architectures on the standard MNIST datasets.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Dec 2017.

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Citing papers per year: 2021: 10; 2022: 5; 2023: 9; 2024: 2; 2025: 2; 2026: 5.

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  1. 2021Supervised quantum machine learning models are kernel methodscited by 199
  2. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  3. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  4. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  5. 2021Tensor networks for unsupervised machine learningcited by 20
  6. 2021Variational inference with a quantum computercited by 18
  7. 2023Tensor networks for interpretable and efficient quantum-inspired machine learningcited by 16
  8. 2022Generative modeling with projected entangled-pair statescited by 14
  9. 2021Tensor networks and efficient descriptions of classical datacited by 13
  10. 2021Matching Point Sets with Quantum Circuit Learningcited by 10
  11. 2024Training-efficient density quantum machine learningcited by 10
  12. 2021Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classificationcited by 9
21 more
  1. 2023Generative Learning of Continuous Data by Tensor Networkscited by 9
  2. 2021Quantum Machine Learning for Financecited by 7
  3. 2023What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglementcited by 4
  4. 2021F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuitscited by 3
  5. 2022Bayesian Learning of Parameterised Quantum Circuitscited by 3
  6. 2022Many-body localized hidden generative modelscited by 3
  7. 2023Generative Invertible Quantum Neural Networkscited by 3
  8. 2021Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelitycited by 2
  9. 2022Deep tensor networks with matrix product operatorscited by 2
  10. 2023Distributive Pre-Training of Generative Modeling Using Matrix-Product Statescited by 2
  11. 2025TabularQGAN: A quantum generative model for tabular data synthesiscited by 2
  12. 2026Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Functioncited by 2
  13. 2023Application-Oriented Benchmarking of Quantum Generative Learning Using QUARKcited by 1
  14. 2023Implementing Quantum Generative Adversarial Network (qGAN) and QCBM in Financecited by 1
  15. 2025A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Datacited by 1
  16. 2022Sample-efficient Quantum Born Machine through Coding Rate Reductioncited by 0
  17. 2023Quantum Generative Modeling using Parameterized Quantum Circuitscited by 0
  18. 2026Quantum Scrambling Born Machinecited by 0
  19. 2026Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimizationcited by 0
  20. 2026HHL with a Coherent Fourier Oracle: A Proof-of-Concept Quantum Architecture for Joint Melody-Harmony Generationcited by 0
  21. 2026QnRL: Quantum-Native Reinforcement Learningcited by 0