mlsanityData to 7 Oct 2026

Variational inference with a quantum computer

arXiv 2103.06720 ↗First posted 11 Mar 2021quant-ph cs.LGcited by 18

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Abstract (arXiv)

Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately, performing exact inference is intractable in general. One alternative is variational inference, where a candidate probability distribution is optimized to approximate the posterior distribution over unobserved variables. For good approximations, a flexible and highly expressive candidate distribution is desirable. In this work, we use quantum Born machines as variational distributions over discrete variables. We apply the framework of operator variational inference to achieve this goal. In particular, we adopt two specific realizations: one with an adversarial objective and one based on the kernelized Stein discrepancy. We demonstrate the approach numerically using examples of Bayesian networks, and implement an experiment on an IBM quantum computer. Our techniques enable efficient variational inference with distributions beyond those that are efficiently representable on a classical computer.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 59 of its 141 references that are in the map. First posted on arXiv 11 Mar 2021.

Builds on

59 of 141 references.

References · 59

  1. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,708
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
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38 more
  1. 2020A rigorous and robust quantum speed-up in supervised machine learningcited by 270
  2. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
  3. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 192
  4. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  5. 2018Quantum generative adversarial networkscited by 128
  6. 2016Learning in Implicit Generative Modelscited by 124
  7. 2017Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networkscited by 107
  8. 2017Quantum machine learning: a classical perspectivecited by 95
  9. 2021Information-theoretic bounds on quantum advantage in machine learningcited by 95
  10. 2015Measuring Sample Quality with Stein's Methodcited by 94
  11. 2020Robust data encodings for quantum classifierscited by 91
  12. 2018Differentiable Learning of Quantum Circuit Born Machinecited by 90
  13. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  14. 2019The Born Supremacy: Quantum Advantage and Training of an Ising Born Machinecited by 75
  15. 2021QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computercited by 65
  16. 2020On the Quantum versus Classical Learnability of Discrete Distributionscited by 57
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  19. 2018Quantum Variational Autoencodercited by 41
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  23. 2017Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machinescited by 33
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  31. 2020Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuitscited by 26
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  38. 2020Quantum machine learning and quantum biomimetics: A perspectivecited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 4; 2024: 3; 2025: 2; 2026: 2.

18 papers.

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  1. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  2. 2023Quantum Deep Hedgingcited by 22
  3. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  4. 2023Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superpositioncited by 8
  5. 2022Conditional Born machine for Monte Carlo event generationcited by 4
  6. 2024Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Datasetcited by 4
  7. 2021QKSA: Quantum Knowledge Seeking Agentcited by 3
  8. 2021F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuitscited by 3
  9. 2022Quantum-Aided Meta-Learning for Bayesian Binary Neural Networks via Born Machinescited by 3
  10. 2022Bayesian Learning of Parameterised Quantum Circuitscited by 3
  11. 2024Tensor tree learns hidden relational structures in data to construct generative modelscited by 3
  12. 2022Quantum Advantage in Variational Bayes Inferencecited by 1
6 more
  1. 2025Bayesian Quantum Orthogonal Neural Networks for Anomaly Detectioncited by 1
  2. 2022Sample-efficient Quantum Born Machine through Coding Rate Reductioncited by 0
  3. 2024Machine Learning for Quantum Computing Specialistscited by 0
  4. 2025Variational Inference for Quantum HyperNetworkscited by 0
  5. 2026Towards unsupervised representation learning for quantum data: quantum models with inference and generationcited by 0
  6. 2026Simulation-Based Quantum System Inference with Neural Posterior Estimationcited by 0