Efficient Quantum Convolutional Neural Networks for Image Classification: Overcoming Hardware Constraints

TL;DR

This work tackles hardware constraints in quantum convolutional neural networks (QCNNs) for image classification by introducing a compact fragment-encoding scheme that enables fully quantum processing of $28\times28$ MNIST images with as few as 49 qubits, and by deploying an automated PQC design framework guided by expressibility, entanglement, and circuit complexity. Bayesian optimization is used to construct an efficient classical CNN baseline and to discover PQC ansätze that balance expressiveness and resource cost. The study contrasts hybrid and fully quantum QCNN architectures, showing that a regular QCNN with fragment encoding and WUE embedding can outperform a classical CNN on a binary task and can achieve strong hardware-validated performance on IBM’s Heron quantum processor ($96.08\%$ accuracy on 0 vs 1). The results underscore potential quantum advantages in practical ML tasks on near-term devices and point to scalable quantum encoding and circuit-design strategies for future larger-scale QCNNs.

Abstract

While classical convolutional neural networks (CNNs) have revolutionized image classification, the emergence of quantum computing presents new opportunities for enhancing neural network architectures. Quantum CNNs (QCNNs) leverage quantum mechanical properties and hold potential to outperform classical approaches. However, their implementation on current noisy intermediate-scale quantum (NISQ) devices remains challenging due to hardware limitations. In our research, we address this challenge by introducing an encoding scheme that significantly reduces the input dimensionality. We demonstrate that a primitive QCNN architecture with 49 qubits is sufficient to directly process $28\times 28$ pixel MNIST images, eliminating the need for classical dimensionality reduction pre-processing. Additionally, we propose an automated framework based on expressibility, entanglement, and complexity characteristics to identify the building blocks of QCNNs, parameterized quantum circuits (PQCs). Our approach demonstrates advantages in accuracy and convergence speed with a similar parameter count compared to both hybrid QCNNs and classical CNNs. We validated our experiments on IBM's Heron r2 quantum processor, achieving $96.08\%$ classification accuracy, surpassing the $71.74\%$ benchmark of traditional approaches under identical training conditions. These results represent one of the first implementations of image classifications on real quantum hardware and validate the potential of quantum computing in this area.

Figures (14)

• Figure 1: Illustration of the hybrid QCNN Type II quantum circuit used for the kernel operation. The input fragments are (1) encoded, (2) processed, and (3) the last qubit is measured.
• Figure 2: Hybrid QCNN Type I hierarchical convolution. First, the receptive field is processed row-wise (1), followed by processing the final column (2).
• Figure 3: Parameterized quantum circuits for a 2-qubit convolution. Circuits 1 to 6 are adapted from previous research papers. Circuit 7 and 8 are from the ansatz search.
• Figure 4: Comparison of $\mathcal{L}_{PQC}$ between the 6 quantum circuits (C) from prior studies and circuits identified through ansatz search (AS) across 4 qubit configurations. For each qubit count, both hybrid QCNN (H) and regular QCNN (R) implementations are shown with distinct background colors.
• Figure 5: Hybrid QCNN Type I (first row) and II (second row) vs CNN baseline for $\{0,1\}$ classification. Comparing models optimized for expressibility (Exp-Opt), entanglement (Ent-Opt), objective function (Obj-Opt), and newly discovered PQC (PQC-Opt).

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof