# Hybrid quantum-classical classifier based on tensor network and variational quantum circuit

arXiv: https://arxiv.org/abs/2011.14651 · HTML: https://mlsanity.com/paper/2011.14651/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 26 of 26)

- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Federated Quantum Long Short-term Memory (FedQLSTM)](https://mlsanity.com/paper/2312.14309/) (2023)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Simulation of a Variational Quantum Perceptron using Grover's Algorithm](https://mlsanity.com/paper/2305.11040/) (2023)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [A preprocessing perspective for quantum machine learning classification advantage using NISQ algorithms](https://mlsanity.com/paper/2208.13251/) (2022)
- [Compositional optimization of quantum circuits for quantum kernels of support vector machines](https://mlsanity.com/paper/2203.13848/) (2022)
- [Scalable Quantum Neural Networks for Classification](https://mlsanity.com/paper/2208.07719/) (2022)
- [BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploading](https://mlsanity.com/paper/2305.00905/) (2023)
- [Quantum Machine Learning in the Cognitive Domain: Alzheimer's Disease Study](https://mlsanity.com/paper/2401.06697/) (2023)
- [Quantum Transfer Learning for Acceptability Judgements](https://mlsanity.com/paper/2401.07777/) (2024)
- [A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity](https://mlsanity.com/paper/2402.15333/) (2024)
- [No-Free-Lunch Theories for Tensor-Network Machine Learning Models](https://mlsanity.com/paper/2412.05674/) (2024)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Quantum Phase Recognition using Quantum Tensor Networks](https://mlsanity.com/paper/2212.06207/) (2022)
- [A Hybrid Classical-Quantum Fine Tuned BERT for Text Classification](https://mlsanity.com/paper/2511.17677/) (2025)
- [Hybrid Variational Quantum-Classical Framework with Adaptive Weighting and Efficiency Assessment](https://mlsanity.com/paper/2609.28491/) (2026)

## Abstract (arXiv)

One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.