Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data

The quantum convolutional neural network (QCNN) is a promising quantum machine learning (QML) model that is expected to achieve quantum advantages in classically intractable problems. However, the QCNN requires a large number of measurements for data learning, limiting its practical applications in large-scale problems. To alleviate this requirement, we propose a novel architecture called split-parallelizing QCNN (sp-QCNN), which exploits the prior knowledge of quantum data to design an efficient model. This architecture draws inspiration from geometric quantum machine learning and targets translationally symmetric quantum data commonly encountered in physics and quantum computing science. By splitting the quantum circuit based on translational symmetry, the sp-QCNN can substantially parallelize the conventional QCNN without increasing the number of qubits and improve the measurement efficiency by an order of the number of qubits. To demonstrate its effectiveness, we apply the sp-QCNN to a quantum phase recognition task and show that it can achieve comparable classification accuracy to the conventional QCNN while considerably reducing the measurement resources required. Due to its high measurement efficiency, the sp-QCNN can mitigate statistical errors in estimating the gradient of the loss function, thereby accelerating the learning process. These results open up new possibilities for incorporating the prior data knowledge into the efficient design of QML models, leading to practical quantum advantages.