arXiv:2405.12625 · Physical Review Research

Quantum resonant dimensionality reduction

Fan Yang, Furong Wang, Xusheng Xu, Pan Gao, Tao Xin, Shijie Wei, Gui‐Lu Long

Published Jan 3, 2025• 5 citations

Abstract

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 dimensionality 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 the 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 / ε 3 to the order of 1 / ε , compared to existing algorithms. Meanwhile, by avoiding quantum phase estimation, the consumed qubits in QRDR is independent on error ε . Therefore, compared with existing algorithms, our algorithm has achieved the optimal performance in terms of time complexity and space complexity. 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 extremely improved the processing efficiency 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.

DOI: 10.1103/physrevresearch.7.013007

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