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Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning

Fan Fan, Yilei Shi, Mihai Datcu, Bertrand Le Saux, Luigi Iapichino, Francesca Bovolo, Silvia Liberata Ullo, Xiao Xiang Zhu

TL;DR

The paper surveys quantum circuit–based learning for classical data, addressing core questions about data encoding, circuit design, and the integration of quantum components in hybrid models. It systematically categorizes data-embedding strategies (e.g., Computational Basis, Amplitude, and Angle Encoding) and reviews kernel-based and neural-network–based quantum learning architectures, including quanvolutional networks and quantum CNNs, with attention to imagery, time-series, and tabular data. It analyzes capabilities (expressivity, learnability, generalizability), observed practical benefits, and resilience to noise, while highlighting hardware-efficient techniques like circuit cutting and shallow architectures. It also outlines emerging paradigms (interpretable design, neural architecture search, distributed circuits) and surveys representative applications in earth observation, healthcare, finance, and astronomy, concluding with future directions for encoding efficiency, systematic circuit design, and robust evaluation benchmarks.

Abstract

Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.

Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning

TL;DR

The paper surveys quantum circuit–based learning for classical data, addressing core questions about data encoding, circuit design, and the integration of quantum components in hybrid models. It systematically categorizes data-embedding strategies (e.g., Computational Basis, Amplitude, and Angle Encoding) and reviews kernel-based and neural-network–based quantum learning architectures, including quanvolutional networks and quantum CNNs, with attention to imagery, time-series, and tabular data. It analyzes capabilities (expressivity, learnability, generalizability), observed practical benefits, and resilience to noise, while highlighting hardware-efficient techniques like circuit cutting and shallow architectures. It also outlines emerging paradigms (interpretable design, neural architecture search, distributed circuits) and surveys representative applications in earth observation, healthcare, finance, and astronomy, concluding with future directions for encoding efficiency, systematic circuit design, and robust evaluation benchmarks.

Abstract

Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
Paper Structure (79 sections, 15 equations, 24 figures)

This paper contains 79 sections, 15 equations, 24 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Quantum Computing
  4. Qubits and their Properties
  5. Quantum Circuits for Computing
  6. Basic Framework of Circuit-based Machine Learning
  7. Quantum Devices and Development
  8. Quantum Circuit Designs for Learning
  9. Data Embedding in Quantum Circuits
  10. Fundamental Encoding Approaches
  11. Computational Basis Encoding
  12. Amplitude Encoding
  13. Angle Encoding
  14. Standard Encoding Strategies
  15. Retrievable Encoding
  16. ...and 64 more sections

Figures (24)

  • Figure 1: Bloch sphere representation of a qubit
  • Figure 2: An example of a quantum circuit with two qubits: H stands for Hadamard gates and $\oplus$ stands for X gate
  • Figure 3: Schematic of a quantum circuit for computation tasks, highlighting the sequential processes of data encoding, quantum state transformation, and measurement
  • Figure 4: Schematic of the quantum circuit-based model, in which the rotation angles $\theta$ of quantum gates are optimized using classical algorithms, while the evolution and measurement of quantum states are executed on a quantum device
  • Figure 5: Basic combinations of quantum computing and machine learning
  • ...and 19 more figures