# QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks

arXiv: https://arxiv.org/abs/2110.03861 · HTML: https://mlsanity.com/paper/2110.03861/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 93 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks](https://mlsanity.com/paper/1312.6229/) (2013)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Tensor-Train Recurrent Neural Networks for Video Classification](https://mlsanity.com/paper/1707.01786/) (2017)
- [Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognition](https://mlsanity.com/paper/2010.13309/) (2020)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Long-term Forecasting using Higher Order Tensor RNNs](https://mlsanity.com/paper/1711.00073/) (2017)
- [Compressing Recurrent Neural Network with Tensor Train](https://mlsanity.com/paper/1705.08052/) (2017)
- [Hybrid quantum-classical classifier based on tensor network and variational quantum circuit](https://mlsanity.com/paper/2011.14651/) (2020)
- [Exploring Deep Hybrid Tensor-to-Vector Network Architectures for Regression Based Speech Enhancement](https://mlsanity.com/paper/2007.13024/) (2020)
- [An efficient quantum algorithm for generative machine learning](https://mlsanity.com/paper/1711.02038/) (2017)
- [Tensor-to-Vector Regression for Multi-channel Speech Enhancement based on Tensor-Train Network](https://mlsanity.com/paper/2002.00544/) (2020)

## Built on by (most cited first, 27 of 27)

- [When BERT Meets Quantum Temporal Convolution Learning for Text Classification in Heterogeneous Computing](https://mlsanity.com/paper/2203.03550/) (2022)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [Classical-to-Quantum Transfer Learning for Spoken Command Recognition Based on Quantum Neural Networks](https://mlsanity.com/paper/2110.08689/) (2021)
- [Learning to Measure Quantum Neural Networks](https://mlsanity.com/paper/2501.05663/) (2025)
- [Federated Quantum Natural Gradient Descent for Quantum Federated Learning](https://mlsanity.com/paper/2209.00564/) (2022)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descent](https://mlsanity.com/paper/2303.08116/) (2023)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2412.08845/) (2024)
- [Quantum Distributed Deep Learning Architectures: Models, Discussions, and Applications](https://mlsanity.com/paper/2202.11200/) (2022)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [Evolutionary Optimization for Designing Variational Quantum Circuits with High Model Capacity](https://mlsanity.com/paper/2412.12484/) (2024)
- [An Introduction to Quantum Reinforcement Learning (QRL)](https://mlsanity.com/paper/2409.05846/) (2024)
- [Adaptive Non-local Observable on Quantum Neural Networks](https://mlsanity.com/paper/2504.13414/) (2025)
- [Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generation](https://mlsanity.com/paper/2505.09653/) (2025)
- [Learning to Program Quantum Measurements for Machine Learning](https://mlsanity.com/paper/2505.13525/) (2025)
- [Compositional optimization of quantum circuits for quantum kernels of support vector machines](https://mlsanity.com/paper/2203.13848/) (2022)
- [Transfer Learning Analysis of Variational Quantum Circuits](https://mlsanity.com/paper/2501.01507/) (2025)
- [Introduction to Quantum Machine Learning and Quantum Architecture Search](https://mlsanity.com/paper/2504.16131/) (2025)
- [Quantum deep Q learning with distributed prioritized experience replay](https://mlsanity.com/paper/2304.09648/) (2023)
- [Quantum Machine Learning: An Interplay Between Quantum Computing and Machine Learning](https://mlsanity.com/paper/2411.09403/) (2024)
- [Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits](https://mlsanity.com/paper/2306.03741/) (2023)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Neural Architecture Search for Quantum Autoencoders](https://mlsanity.com/paper/2511.19246/) (2025)

## Abstract (arXiv)

The advent of noisy intermediate-scale quantum (NISQ) computers raises a crucial challenge to design quantum neural networks for fully quantum learning tasks. To bridge the gap, this work proposes an end-to-end learning framework named QTN-VQC, by introducing a trainable quantum tensor network (QTN) for quantum embedding on a variational quantum circuit (VQC). The architecture of QTN is composed of a parametric tensor-train network for feature extraction and a tensor product encoding for quantum embedding. We highlight the QTN for quantum embedding in terms of two perspectives: (1) we theoretically characterize QTN by analyzing its representation power of input features; (2) QTN enables an end-to-end parametric model pipeline, namely QTN-VQC, from the generation of quantum embedding to the output measurement. Our experiments on the MNIST dataset demonstrate the advantages of QTN for quantum embedding over other quantum embedding approaches.