# A Quantum Information Theoretic Approach to Tractable Probabilistic Models

arXiv: https://arxiv.org/abs/2506.01824 · HTML: https://mlsanity.com/paper/2506.01824/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 19 of 19)

- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Subtractive Mixture Models via Squaring: Representation and Learning](https://mlsanity.com/paper/2310.00724/) (2023)
- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)
- [Sum of Squares Circuits](https://mlsanity.com/paper/2408.11778/) (2024)
- [On Tractable Computation of Expected Predictions](https://mlsanity.com/paper/1910.02182/) (2019)
- [On the Expressive Efficiency of Sum Product Networks](https://mlsanity.com/paper/1411.7717/) (2014)
- [HyperSPNs: Compact and Expressive Probabilistic Circuits](https://mlsanity.com/paper/2112.00914/) (2021)
- [On the Relationship Between Monotone and Squared Probabilistic Circuits](https://mlsanity.com/paper/2408.00876/) (2024)
- [On the Relationship Between Probabilistic Circuits and Determinantal Point Processes](https://mlsanity.com/paper/2006.15233/) (2020)
- [Probabilistic Neural Circuits](https://mlsanity.com/paper/2403.06235/) (2024)
- [Probabilistic Generating Circuits -- Demystified](https://mlsanity.com/paper/2404.02912/) (2024)
- [On Faster Marginalization with Squared Circuits via Orthonormalization](https://mlsanity.com/paper/2412.07883/) (2024)
- [Quantum Algorithms for Weighted Constrained Sampling and Weighted Model Counting](https://mlsanity.com/paper/2407.12816/) (2024)

## Built on by (most cited first, 1 of 1)

- [How to Square Tensor Networks and Circuits Without Squaring Them](https://mlsanity.com/paper/2512.17090/) (2025)

## Abstract (arXiv)

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.