# Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach

arXiv: https://arxiv.org/abs/2111.01536 · HTML: https://mlsanity.com/paper/2111.01536/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 72 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [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)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Quantum Tensor Networks, Stochastic Processes, and Weighted Automata](https://mlsanity.com/paper/2010.10653/) (2020)
- [Expressiveness and Learning of Hidden Quantum Markov Models](https://mlsanity.com/paper/1912.02098/) (2019)
- [Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/1710.09016/) (2017)
- [Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models](https://mlsanity.com/paper/2105.06285/) (2021)
- [Learning Quantum Graphical Models using Constrained Gradient Descent on the Stiefel Manifold](https://mlsanity.com/paper/1903.03730/) (2019)
- [Enhancing speaker identification performance under the shouted talking condition using second-order circular hidden Markov models](https://mlsanity.com/paper/1706.09716/) (2017)

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

- [Robust Iterative Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/2510.23237/) (2025)

## Abstract (arXiv)

In this paper, we propose circular Hidden Quantum Markov Models (c-HQMMs), which can be applied for modeling temporal data in quantum datasets (with classical datasets as a special case). We show that c-HQMMs are equivalent to a constrained tensor network (more precisely, circular Local Purified State with positive-semidefinite decomposition) model. This equivalence enables us to provide an efficient learning model for c-HQMMs. The proposed learning approach is evaluated on six real datasets and demonstrates the advantage of c-HQMMs on multiple datasets as compared to HQMMs, circular HMMs, and HMMs.