Resource-efficient equivariant quantum convolutional neural networks

TL;DR

This paper introduces a resource-efficient equivariant quantum convolutional neural network model that leverages symmetry and circuit splitting to reduce measurement costs and improve trainability on near-term quantum devices.

Contribution

It proposes an equivariant split-parallelizing QCNN that encodes general symmetries and enhances measurement efficiency through circuit splitting, addressing resource limitations.

Findings

The model reduces measurement resources needed for training and inference.

It maintains high trainability and avoids barren plateaus.

Numerical experiments show effective training and generalization with fewer resources.

Abstract

Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum devices remains challenging due to limited computational resources. This study proposes a resource-efficient model of equivariant quantum convolutional neural networks (QCNNs) called equivariant split-parallelizing QCNN (sp-QCNN). Using a group-theoretical approach, we encode general symmetries into our model beyond the translational symmetry addressed by previous sp-QCNNs. We achieve this by splitting the circuit at the pooling layer while preserving symmetry. This splitting structure effectively parallelizes QCNNs to improve measurement efficiency in estimating the expectation value of an observable and its gradient by order of the number of qubits. Our model also exhibits high trainability and generalization performance, including the absence of barren plateaus. Numerical experiments demonstrate that the equivariant sp-QCNN can be trained and generalized with fewer measurement resources than a conventional equivariant QCNN in a noisy quantum data classification task. Our results contribute to the advancement of practical quantum machine learning algorithms.