Subspace Preserving Quantum Convolutional Neural Network Architectures

TL;DR

This paper introduces a novel quantum convolutional neural network architecture based on subspace preserving quantum circuits, demonstrating polynomial speed-up and efficient image classification with fewer parameters.

Contribution

It proposes a new quantum CNN model utilizing Hamming weight preserving circuits, including convolutional and pooling layers, with an open-source simulation library.

Findings

Significant polynomial runtime advantages over classical deep learning.

Effective performance on complex image classification tasks.

Fewer parameters needed compared to classical architectures.

Abstract

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.