[Paper Review] Quantum machine learning for image classification

Arsenii Senokosov, Alexander Sedykh+3 more|arXiv (Cornell University)|Apr 18, 2023

Quantum Computing Algorithms and ArchitectureComputer Science74 references9 citations

TL;DR

The paper presents two hybrid quantum-classical neural networks for MNIST digit classification: HQNN-Parallel with parallel VQCs achieving 99.21% test accuracy, and HQNN-Quanv with a quantum quanvolutional layer achieving 67% accuracy, both with significantly fewer trainable parameters than classical counterparts.

ABSTRACT

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum-classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

Motivation & Objective

• Motivate the use of quantum effects to enhance image classification beyond classical deep learning.
• Propose two hybrid quantum-classical models (HQNN-Parallel and HQNN-Quanv) for MNIST digit recognition.
• Evaluate and compare performance and parameter efficiency against classical CNN baselines.

Proposed method

• Use a classical convolutional front-end to extract features, followed by a quantum-dense block with parallel VQCs (HQNN-Parallel).
• Encode classical features into quantum states via angle embedding and train variational parameters using the parameter-shift rule; concatenate VQC outputs for a final classical dense layer.
• Introduce a quanvolutional layer (HQNN-Quanv) where quantum filters of size n×n act as convolutional kernels via angle embedding, variational gates, and measurement to produce output channels fed into a dense layer.
• Train all parameters end-to-end using cross-entropy loss and backpropagation for classical parts; apply PennyLane for quantum gradients (parameter-shift rule) and PyTorch for classical parts.
• Compare HQNN-Parallel to a CNN with equivalent architecture and fewer parameters; compare HQNN-Quanv to CNNs with small and large kernels, controlling for number of trainable parameters.

Figure 1: Examples of images from the MNIST dataset

Experimental results

Research questions

• RQ1 Can hybrid quantum-classical networks improve image classification accuracy on MNIST compared to classical CNNs with similar architecture and parameter counts?
• RQ2 What is the impact of parallel VQCs versus a quanvolutional quantum layer on classification performance and parameter efficiency?
• RQ3 How trainable are the quantum circuit parameters, and can end-to-end training enhance learning on image data?
• RQ4 How do Quantum Neural Networks perform with constrained dataset sizes and simplified architectures?

Key findings

• HQNN-Parallel achieves 99.21% test accuracy on MNIST, outperforming a CNN with ~8× more parameters (98.71%).
• HQNN-Parallel uses eight times fewer parameters than the classical CNN in the comparison.
• HQNN-Quanv achieves 67% ±1% test accuracy, comparable to CNN4 (66% ±2%) but with four times fewer trainable parameters in the first layer.
• HQNN-Quanv outperforms CNN1 (53% ±2%) when matched for parameter counts in the filters.
• All parameters in both models are trainable, highlighting the potential of hybrid quantum-classical approaches for image classification.

Figure 2: Examples of ambiguous images from the MNIST dataset.