A research codebase for learning density operator latent variable models
This repository contains a reference implementation of the Density Operator Expectation Maximization framework - a generalization of the classical Expectation-Maximization (EM) algorithm for latent variable models using Density Operators, the mathematical foundation of quantum mechanics.
It includes:
- Core algorithm for DO-EM training
- Large models trained using Contrastive Divergence (CD) to approximate M-Step update
- Models: Quantum Boltzmann Machines, Quantum interleaved Deep Boltzmann Machines, Quantum Gaussian-Bernoulli RBMs
- Evaluation utilities and benchmarks
DO-EM leverages Quantum Information Theoretic tools like the Petz recovery map in place of traditional probabilistic conditional inference.
Refer to the Reproducability Guide to install necessary packages and reproduce the experiments presented in this paper
Please cite the paper as
@article{vishnu2025doem,
title = {Density Operator Expectation Maximization},
author = {Vishnu, Adit and Shastry, Abhay and Kashyap, Dhruva and Bhattacharyya, Chiranjib},
year = {2025},
eprint = {2507.22786},
archivePrefix = {arXiv},
primaryClass = {cs.LG},
url = {https://arxiv.org/abs/2507.22786},
doi = {10.48550/arXiv.2507.22786}
}