Quantum Neural Networks: A Comparative Study on MNIST Dataset

This repository accompanies the research paper "Quantum Neural Networks: A Comparative Study of Quantum and Classical Neural Networks on the MNIST Dataset" by Shahaf Brenner, Anna Payne, Trinidad Roca, Juan Diego Fernandez, Sergio Verdugo, Noah Valderrama, and Pedro Torrado.

Overview

This project explores the performance of Quantum Neural Networks (QNNs) and Classical Neural Networks (NNs) on a subset of the MNIST dataset. It evaluates:

• Training speed, accuracy, and loss differences.
• Quantum advantages such as superposition and entanglement.
• QNNs’ performance under resource-constrained and real-world conditions.

By leveraging TensorFlow Quantum, the research highlights the potential of QNNs for machine learning tasks and discusses their scalability and current limitations in a local setting.

Project Structure

• data_preprocess.py: Scripts for MNIST data cleaning and resizing (28x28 → 4x4).
• qnn.py: Implementation of Quantum Neural Network (QNN) using Cirq and TensorFlow Quantum.
• nn.py: Implementation of a classical neural network for comparison.
• qnn_train.py: Training the QNN model.
• nn_qnn_compare.py: Scripts for running and evaluating experiments across epochs and models.
• QNN_VS_Classic_NN.ipynb: Jupyter notebook for visualizing entire model performance, including accuracy and loss graphs.

Key Features

Data Preprocessing

• Resizing MNIST images to 4x4 for quantum hardware compatibility.
• Binarization of pixel values for qubit mapping.

Model Architectures

• Classical Neural Network: Simple feed-forward NN with 37 parameters.
• Quantum Neural Network: Quantum circuit with 32 parameters leveraging quantum gates for feature representation.

Comparison Metrics

• Accuracy, loss, and scalability.
• Testing scenarios with varying epochs (3, 5, and 10).

Setup and Installation

Dependencies

• Python 3.9+
• TensorFlow Quantum
• Cirq
• TensorFlow
• NumPy
• Matplotlib

How to Run

• python data_preproces.py
• python qnn.py
• python nn.py
• python nn_qnn_compare.py

Results Summary

• Testing Accuracy:
  • Full QNN: 90.6%
  • Fair NN: 82.7%
• Loss Comparison:
  • Full QNN: 0.345
  • Fair NN: 0.264

QNNs demonstrated potential advantages in noisy and high-dimensional data scenarios, while classical models excelled in low-noise, computationally simple tasks.

Future Work

Future research will explore:

• Leveraging more advanced quantum hardware with higher qubit counts.
• Expanding to complex and noisy datasets.
• Integrating hybrid quantum-classical models for feature extraction and classification.
• Integrating IBM's Quantum Experience platform

Citation

If you use this repository or reference our paper, please cite: "Quantum Neural Networks: A Comparative Study of Quantum and Classical Neural Networks on the MNIST Dataset"