Multi-Class Quantum Convolutional Neural Networks

TL;DR

This paper addresses multi-class classification of classical data using a quantum convolutional neural network (QCNN) implemented in PennyLane and trained via cross-entropy optimization. It introduces two data-encoding strategies (amplitude and angle encoding) and a QCNN architecture with preconvolutional preprocessing, convolutional and pooling layers, and measurement, evaluating on MNIST across 4, 6, 8, and 10 classes. The results show that, while 4-class performance is comparable to a classical CNN, the QCNN outperforms the classical baseline for 6–10 classes with substantially fewer parameters, and remains robust when trained on smaller datasets. The work highlights the potential of QCNNs for scalable, low-parameter multi-class classification in information retrieval contexts and outlines avenues for architectural and measurement improvements, as well as generalization studies.

Abstract

Classification is particularly relevant to Information Retrieval, as it is used in various subtasks of the search pipeline. In this work, we propose a quantum convolutional neural network (QCNN) for multi-class classification of classical data. The model is implemented using PennyLane. The optimization process is conducted by minimizing the cross-entropy loss through parameterized quantum circuit optimization. The QCNN is tested on the MNIST dataset with 4, 6, 8 and 10 classes. The results show that with 4 classes, the performance is slightly lower compared to the classical CNN, while with a higher number of classes, the QCNN outperforms the classical neural network.

Figures (6)

• Figure 1: General structure of the quantum convolutional neural network for 10-class classification. It consists of several steps: encoding of the classical data ($E$), preconvolutional filters ($F^{(n)}_1$), convolution filters ($F_2$), pooling layer ($P$) and measurement.
• Figure 2: Parameterized quantum circuit used in the convolutional layer. $R_i(\theta)$ is a rotation around the $i$ axis by an angle of $\theta$. $U3(\theta, \phi, \lambda)$ is an arbitrary single-qubit gate that can be expressed as $U3(\theta, \phi, \lambda) = R_z(\phi)R_x(-\pi/2)R_z(\theta)R_x(\pi/2)R_z(\lambda)$.
• Figure 3: Parameterized quantum circuit used for implementing the pooling operation hur2022quantum.
• Figure 4: Comparison of the classification accuracy between the QCNN using amplitude and angle encoding. The evaluation involves increasing the number of epochs and varying the number of classes, with learning rate equal to 0.01. In the 4-class case, classes 0 to 3 are considered, while for 6 classes, classes from 0 to 5 are taken into account, and for 8 classes, classes 0 to 7 are included.
• Figure 5: Comparison of the classification accuracy of CNN and QCNN. The evaluation involves increasing the number of epochs and varying the number of classes, with learning rate equal to 0.01. In the 4-class case, classes 0 to 3 are considered, while for 6 classes, classes from 0 to 5 are taken into account, and for 8 classes, classes 0 to 7 are included.