mlsanityData to 7 Oct 2026

Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression

arXiv 2206.04804 ↗First posted 8 Jun 2022quant-ph cs.AI cs.LGcited by 26

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Abstract (arXiv)

The noisy intermediate-scale quantum (NISQ) devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end quantum neural network, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz (PL) condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 25 of its 55 references that are in the map. First posted on arXiv 8 Jun 2022.

Builds on

25 of 55 references.

References · 25

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Variational Quantum Algorithmscited by 687
  3. 2018Barren plateaus in quantum neural network training landscapescited by 624
  4. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  5. 2020Power of data in quantum machine learningcited by 336
  6. 2019Parameterized quantum circuits as machine learning modelscited by 330
  7. 2016Quantum Machine Learningcited by 325
  8. 2015Tensorizing Neural Networkscited by 246
  9. 2019Variational Quantum Circuits for Deep Reinforcement Learningcited by 165
  10. 2019Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methodscited by 148
  11. 2018Differentially Private Empirical Risk Minimization Revisited: Faster and More Generalcited by 127
  12. 2020Experimental Quantum Generative Adversarial Networks for Image Generationcited by 83
13 more
  1. 2021Reinforcement learning for optimization of variational quantum circuit architecturescited by 76
  2. 2018Towards Quantum Machine Learning with Tensor Networkscited by 74
  3. 2017Tensor-Train Recurrent Neural Networks for Video Classificationcited by 59
  4. 2020Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognitioncited by 56
  5. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 49
  6. 2022When BERT Meets Quantum Temporal Convolution Learning for Text Classification in Heterogeneous Computingcited by 40
  7. 2020On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regressioncited by 33
  8. 2021QTN-VQC: An End-to-End Learning framework for Quantum Neural Networkscited by 27
  9. 2021Classical-to-Quantum Transfer Learning for Spoken Command Recognition Based on Quantum Neural Networkscited by 19
  10. 2018A Grover-search Based Quantum Learning Scheme for Classificationcited by 12
  11. 2020Analyzing Upper Bounds on Mean Absolute Errors for Deep Neural Network Based Vector-to-Vector Regressioncited by 10
  12. 2022Exploiting Low-Rank Tensor-Train Deep Neural Networks Based on Riemannian Gradient Descent With Illustrations of Speech Processingcited by 10
  13. 2020Tensor-to-Vector Regression for Multi-channel Speech Enhancement based on Tensor-Train Networkcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 10; 2024: 5; 2025: 4; 2026: 5.

26 papers.

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  1. 2022Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noisecited by 17
  2. 2023Federated Quantum Machine Learning with Differential Privacycited by 17
  3. 2023Tensor networks for quantum machine learningcited by 16
  4. 2022Federated Quantum Natural Gradient Descent for Quantum Federated Learningcited by 14
  5. 2023Parallel Hybrid Networks: an interplay between quantum and classical neural networkscited by 14
  6. 2023Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descentcited by 14
  7. 2023Efficient quantum recurrent reinforcement learning via quantum reservoir computingcited by 14
  8. 2023Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuitscited by 9
  9. 2023Quantum Federated Learning With Quantum Networkscited by 8
  10. 2024Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Surveycited by 7
  11. 2025Feedback-driven recurrent quantum neural network universalitycited by 5
  12. 2025TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computingcited by 5
14 more
  1. 2023A hybrid quantum-classical fusion neural network to improve protein-ligand binding affinity predictions for drug discoverycited by 4
  2. 2024Lean classical-quantum hybrid neural network model for image classificationcited by 4
  3. 2024Quantum Machine Learning: An Interplay Between Quantum Computing and Machine Learningcited by 2
  4. 2023Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuitscited by 1
  5. 2023Statistical Analysis of Quantum State Learning Process in Quantum Neural Networkscited by 1
  6. 2024Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuitscited by 1
  7. 2024Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noisecited by 1
  8. 2025VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learningcited by 1
  9. 2025Joint Tensor-Train Parameterization for Efficient and Expressive Low-Rank Adaptationcited by 1
  10. 2026Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learningcited by 1
  11. 2026Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuitscited by 0
  12. 2026Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processingcited by 0
  13. 2026Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligencecited by 0
  14. 2026Multitask Learning for Earth Observation Data Classification with Hybrid Quantum Networkcited by 0