A quantum convolutional neural network (QCNN) is a promising quantum machine
learning (QML) model to achieve quantum advantages in classically intractable
problems. However, QCNN requires a large number of measurements for data
learning, limiting its practical applications for large-scale problems. To
relieve this requirement, we propose a novel architecture called
split-parallelizing QCNN (sp-QCNN), which exploits the prior knowledge of
quantum data for designing efficient circuits. This architecture draws
inspiration from geometric quantum machine learning and targets translationally
symmetric quantum data commonly encountered in condensed matter physics. By
splitting the quantum circuit based on translational symmetry, sp-QCNN
substantially parallelizes conventional QCNN without increasing the number of
qubits and further improves the measurement efficiency by an order of the
number of qubits. To demonstrate its effectiveness, we apply sp-QCNN to a
quantum phase recognition task and show that it can achieve similar performance
to conventional QCNN while considerably reducing the measurement resources
required. Due to its high measurement efficiency, 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 knowledge of data into the efficient design of QML
models, leading to practical quantum advantages.

本文提出了一种 split-parallelizing QCNN 架构，通过基于平移对称性拆分量子电路，从而实现了对传统 QCNN 的显著并行，并进一步将计算开销降低到量子位数的数量级，从而改善了量子机器学习的成果表现，为实用性提供了新的可能性，该方法在具有传递对称性的量子数据中的应用效果显著。