# Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States

arXiv: https://arxiv.org/abs/2106.08334 · HTML: https://mlsanity.com/paper/2106.08334/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 82 references that are in the map.
- First posted on arXiv 15 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Learning to Pivot with Adversarial Networks](https://mlsanity.com/paper/1611.01046/) (2016)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [MadMiner: Machine learning-based inference for particle physics](https://mlsanity.com/paper/1907.10621/) (2019)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [Constraining Effective Field Theories with Machine Learning](https://mlsanity.com/paper/1805.00013/) (2018)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [Tensor Networks for Medical Image Classification](https://mlsanity.com/paper/2004.10076/) (2020)
- [Modeling Sequences with Quantum States: A Look Under the Hood](https://mlsanity.com/paper/1910.07425/) (2019)
- [Entanglement and Tensor Networks for Supervised Image Classification](https://mlsanity.com/paper/2007.06082/) (2020)
- [A Multi-Scale Tensor Network Architecture for Classification and Regression](https://mlsanity.com/paper/2001.08286/) (2020)
- [Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification](https://mlsanity.com/paper/2101.03154/) (2021)
- [Matrix Product State for Feature Extraction of Higher-Order Tensors](https://mlsanity.com/paper/1503.00516/) (2015)
- [Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecasting](https://mlsanity.com/paper/2105.04983/) (2021)

## Built on by (most cited first, 9 of 9)

- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC](https://mlsanity.com/paper/2506.00102/) (2025)
- [Jet Discrimination with Quantum Complete Graph Neural Network](https://mlsanity.com/paper/2403.04990/) (2024)
- [The role of data embedding in quantum autoencoders for improved anomaly detection](https://mlsanity.com/paper/2409.04519/) (2024)
- [Hardware-Aware Tensor Networks for Real-Time Quantum-Inspired Anomaly Detection at Particle Colliders](https://mlsanity.com/paper/2603.26604/) (2026)
- [Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach](https://mlsanity.com/paper/2604.06541/) (2026)

## Abstract (arXiv)

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine learning techniques, thereby facilitating an improved interpretability of neural networks. This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier. We show that entanglement entropy can be used to interpret what a network learns, which can be used to reduce the complexity of the network and feature space without loss of generality or performance. For the optimisation of the network, we compare the Density Matrix Renormalization Group (DMRG) algorithm to stochastic gradient descent (SGD) and propose a joined training algorithm to harness the explainability of DMRG with the efficiency of SGD.