# Tensor Ring Optimized Quantum-Enhanced Tensor Neural Networks

arXiv: https://arxiv.org/abs/2310.01515 · HTML: https://mlsanity.com/paper/2310.01515/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 82 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [Deep Learning for Hyperspectral Image Classification: An Overview](https://mlsanity.com/paper/1910.12861/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Learning Graph Convolutional Network for Skeleton-based Human Action Recognition by Neural Searching](https://mlsanity.com/paper/1911.04131/) (2019)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [Compressing Recurrent Neural Networks with Tensor Ring for Action Recognition](https://mlsanity.com/paper/1811.07503/) (2018)
- [Convolutional Rectifier Networks as Generalized Tensor Decompositions](https://mlsanity.com/paper/1603.00162/) (2016)
- [Einconv: Exploring Unexplored Tensor Network Decompositions for Convolutional Neural Networks](https://mlsanity.com/paper/1908.04471/) (2019)
- [Tensor Contraction Layers for Parsimonious Deep Nets](https://mlsanity.com/paper/1706.00439/) (2017)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Robust Kronecker Component Analysis](https://mlsanity.com/paper/1801.06432/) (2018)
- [Qutrit-inspired Fully Self-supervised Shallow Quantum Learning Network for Brain Tumor Segmentation](https://mlsanity.com/paper/2009.06767/) (2020)
- [Random Quantum Neural Networks (RQNN) for Noisy Image Recognition](https://mlsanity.com/paper/2203.01764/) (2022)
- [Interaction Decompositions for Tensor Network Regression](https://mlsanity.com/paper/2208.06029/) (2022)

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

- [Alz-QNet: A Quantum Regression Network for Studying Alzheimer's Gene Interactions](https://mlsanity.com/paper/2508.04743/) (2025)

## Abstract (arXiv)

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters on classical implementations. To address this issue, a multi-layer design of a Tensor Ring optimized variational Quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as Tensor Ring optimized Quantum-enhanced tensor neural Networks (TR-QNet). TR-QNet parameters are optimized through the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is assessed on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. On quantum simulations, the proposed TR-QNet achieves promising accuracy of 94.5%, 86.16%, and 83.54% on the Iris, MNIST, and CIFAR-10 datasets, respectively. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github:https://github.com/konar1987/TR-QNet/