Quantum Resonant Dimensionality Reduction and Its Application in Quantum Machine Learning

Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here, we propose a quantum resonant dimension reduction (QRDR) algorithm based on the quantum resonant transition to reduce the dimension of input data and accelerate the quantum machine learning algorithms. After QRDR, the dimension of input data $N$ can be reduced into desired scale $R$, and the effective information of the original data will be preserved correspondingly, which will reduce the computational complexity of subsequent quantum machine learning algorithms or quantum storage. QRDR operates with polylogarithmic time complexity and reduces the error dependency from the order of $1/\epsilon^3$ to the order of $1/\epsilon$, compared to existing algorithms. We demonstrate the performance of our algorithm combining with two types of quantum classifiers, quantum support vector machines and quantum convolutional neural networks, for classifying underwater detection targets and quantum many-body phase respectively. The simulation results indicate that reduced data improved the processing efficiency and accuracy following the application of QRDR. As quantum machine learning continues to advance, our algorithm has the potential to be utilized in a variety of computing fields.