# Modeling Sequences with Quantum States: A Look Under the Hood

arXiv: https://arxiv.org/abs/1910.07425 · HTML: https://mlsanity.com/paper/1910.07425/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2019.

## Built on by (most cited first, 19 of 19)

- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Quantum-Inspired Tensor Neural Networks for Partial Differential Equations](https://mlsanity.com/paper/2208.02235/) (2022)
- [Generalization Metrics for Practical Quantum Advantage in Generative Models](https://mlsanity.com/paper/2201.08770/) (2022)
- [Generative Modeling via Hierarchical Tensor Sketching](https://mlsanity.com/paper/2304.05305/) (2023)
- [Explainable Natural Language Processing with Matrix Product States](https://mlsanity.com/paper/2112.08628/) (2021)
- [Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework](https://mlsanity.com/paper/2106.15666/) (2021)
- [Generative Modeling via Tree Tensor Network States](https://mlsanity.com/paper/2209.01341/) (2022)
- [High-dimensional density estimation with tensorizing flow](https://mlsanity.com/paper/2212.00759/) (2022)
- [Many-body localized hidden generative models](https://mlsanity.com/paper/2207.02346/) (2022)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Quantum-Inspired Tensor Neural Networks for Option Pricing](https://mlsanity.com/paper/2212.14076/) (2022)
- [Minimal Effective Theory for Phonotactic Memory: Capturing Local Correlations due to Errors in Speech](https://mlsanity.com/paper/2309.02466/) (2023)
- [Application of Tensor Neural Networks to Pricing Bermudan Swaptions](https://mlsanity.com/paper/2304.09750/) (2023)
- [Entangling Machine Learning with Quantum Tensor Networks](https://mlsanity.com/paper/2403.12969/) (2024)
- [LiQSS: Post-Transformer Linear Quantum-Inspired State-Space Tensor Networks for Real-Time 6G](https://mlsanity.com/paper/2601.12375/) (2026)

## Abstract (arXiv)

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the even-parity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset used in training.