Bridging Classical and Quantum Machine Learning

Welcome to Bridging Classical and Quantum Machine Learning, a repository that combines Qiskit basics with PyTorch-based quantum–classical hybrid experiments. This project introduces how to leverage knowledge distillation to transfer capabilities from classical neural networks to resource-constrained quantum neural networks. In addition, the repository provides Qiskit fundamentals through the Qiskit Basics.ipynb notebook to help you get started with quantum computing concepts and simulations.

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Table of Contents

1. Motivation
2. Architecture and Approach
   • Knowledge Distillation Method
   • Dimensionality Techniques
3. Qiskit Basics
4. Project Structure
5. Installation and Setup
6. Usage
7. Experiments
   • MNIST
   • FashionMNIST
8. Results
9. Citation
10. License

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Motivation

Quantum neural networks (QNNs) promise a new frontier in machine learning, potentially surpassing classical models when they have a similar number of parameters. However, challenges such as limited qubit availability, decoherence, and hardware noise make large-scale training of quantum models difficult.

This project addresses these obstacles by transferring knowledge from large, well-trained classical neural networks to quantum student models. Through knowledge distillation, we bypass the requirement of training large quantum networks, making it more feasible to reap the benefits of quantum computing for tasks like image classification.

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Architecture and Approach

Knowledge Distillation Method

In our paper, “Bridging Classical and Quantum Machine Learning: Knowledge Transfer From Classical to Quantum Neural Networks Using Knowledge Distillation,” we show how a frozen classical CNN (teacher) transfers knowledge to a smaller quantum network (student). Below is a high-level diagram illustrating the overall training scheme:

We compare our classical-to-quantum knowledge distillation approach to (1) classical-to-classical and (2) quantum-to-quantum distillation methods:

1. Teacher Model (Classical, Frozen)
   • Typically a large CNN (e.g., LeNet, AlexNet).
2. Student Model (Quantum, Trainable)
   • A QNN with significantly fewer trainable parameters.
3. Distillation Loss
   • Minimizes KL divergence between teacher’s and student’s output logits.

Dimensionality Techniques

Because quantum circuits can only handle a limited number of qubits, we must reduce input dimensionality before encoding data into a quantum circuit. We experiment with several strategies:

1. Fully Connected (Flatten + FC):
   • Flatten the image, project to (2^Q) features for (Q) qubits.
2. Average/Max Pooling:
   • Divide the image into (2^Q) regions and pool values.
3. Center Crop:
   • Crop the central (N \times N) patch with (N^2 = 2^Q).
4. PCA:
   • Use Principal Component Analysis to extract (2^Q) components.

Below is an example of the error rates for different dimensionality strategies across MNIST, FashionMNIST, and CIFAR10 for 4-qubit and 8-qubit QNNs:

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Qiskit Basics

Alongside our quantum–classical experiments, this repository includes a Jupyter notebook named Qiskit Basics.ipynb, where you can learn:

• How to create quantum circuits using Qiskit
• Fundamental quantum operations (gates, measurements)
• Running quantum circuits on simulators
• (Optionally) deploying circuits on real quantum hardware

This serves as a gentle introduction to quantum computing concepts that underpin the experiments in the student QNN.

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Project Structure

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├── Qiskit Basics.ipynb                # Fundamentals of Qiskit
├── MNIST Experiments
│   ├── Teachers                       # Classical CNN teacher notebooks
│   ├── Baseline students             # Quantum students without distillation
│   └── Distillation on students      # Quantum students with knowledge distillation
├── FashionMNIST Experiments
│   ├── Teachers
│   ├── Baseline students
│   └── Distillation on students
├── ss1.png                            # Architecture diagram
├── ss2.png                            # Motivation & method comparison diagram
├── ss3.png                            # Dimensionality reduction methods
├── ss4.png                            # Error comparison chart
└── README.md                          # You are here!

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Installation and Setup

To run the experiments and Qiskit tutorials, you need:

• Python 3.7 or higher
• PyTorch 1.8 or higher
• Qiskit 0.25 or higher
• TorchQuantum 0.1.0 or higher
• Jupyter Notebook or Jupyter Lab

Quick Installation

pip install torch            # For PyTorch
pip install qiskit           # For Qiskit
pip install torchquantum     # For TorchQuantum
pip install jupyter          # For notebooks

Optional: Virtual Environment

It’s recommended to use a virtual environment:

python -m venv venv
source venv/bin/activate  # or venv\Scripts\activate on Windows

Then proceed with the installations within your virtual environment.

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Usage

1. Clone the Repository

   git clone https://github.com/your_username/quantum-machine-learning.git
   cd quantum-machine-learning

2. Launch Jupyter

   jupyter notebook  # or jupyter lab

3. Open Notebooks

   • Qiskit Basics.ipynb (to learn essential quantum operations).
   • MNIST Experiments or FashionMNIST Experiments notebooks (for classical teacher training, baseline quantum models, and knowledge-distilled quantum models).

If you prefer Google Colab, simply upload the notebooks and select the appropriate runtime.

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Experiments

MNIST

1. Teachers
   • Train classical CNNs (LeNet, etc.) on MNIST.
2. Baseline Students
   • Train quantum models without using distillation.
3. Distillation on Students
   • Transfer knowledge from the frozen classical teacher to the quantum student.

FashionMNIST

Follow the same process as MNIST but with FashionMNIST data:

1. Teachers
2. Baseline Students
3. Distillation on Students

These steps highlight how knowledge distillation improves QNN accuracy across different datasets.

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Results

• MNIST: Average quantum model accuracy improves by 0.80% with distillation.
• FashionMNIST: Average quantum model accuracy improves by 5.40% with distillation.
• CIFAR10 (in some ablation studies): Also shows enhancement, although absolute performance is more challenging due to dataset complexity.

Refer to the Error Comparison chart (ss4.png) for a visual summary of various dimensionality reduction strategies and 4-qubit/8-qubit experiments.

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Citation

If you find this repository useful in your research, please consider citing our work:

@article{hasan2023bridging,
  title={Bridging Classical and Quantum Machine Learning: Knowledge Transfer From Classical to Quantum Neural Networks Using Knowledge Distillation},
  author={Hasan, Mohammad Junayed and Mahdy, MRC},
  journal={arXiv preprint arXiv:2311.13810},
  year={2023}
}

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License

This project is licensed under the MIT License. See the LICENSE file for details.

Happy Quantum Coding! If you have any questions or suggestions, feel free to open an issue or submit a pull request.

© 2025 Mohammad Junayed Hasan

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