Quantum angle encoding with learnable rotation applied to quantum–classical convolutional neural networks

Quantum Machine Learning (QML) has experienced rapid progress in recent years due to the development of Noisy Intermediate-Scale Quantum (NISQ) devices and quantum simulators. Two key elements must be minimized To maintain acceptable computational complexity in QML: the number of qubits required to encode classical data and the number of quantum gates. This paper proposes a novel angle encoding with learnable rotation to drastically reduce the qubits and circuit depth from O(N) to O(⌈log2(N)⌉) qubits, and only N parameterized gates, where N is the input size. Additionally, an extended quantum convolutional layer is introduced with multiple quantum circuits (quantum kernel) that allow for the configuration of any arbitrary size, stride, and dilation analogous to a classical convolutional layer. The proposed quantum convolutional layer learns multiple feature maps with a single quantum kernel while reducing computational cost by employing angle encoding with learnable rotation. Extensive experiments were performed by comparing diverse types of quantum convolutional configurations in a Quantum Convolutional Neural Network (QCNN) over a balanced subset of the MNIST and Fashion-MNIST datasets, achieving an accuracy of 0.90 and 0.7850, respectively.