Quantum Multi-Round Resonant Transition Algorithm

Author:

Yang FanORCID,Chen Xinyu,Zhao DafaORCID,Wei Shijie,Wen Jingwei,Wang Hefeng,Xin Tao,Long Guilu

Abstract

Solving the eigenproblems of Hermitian matrices is a significant problem in many fields. The quantum resonant transition (QRT) algorithm has been proposed and demonstrated to solve this problem using quantum devices. To better realize the capabilities of the QRT with recent quantum devices, we improve this algorithm and develop a new procedure to reduce the time complexity. Compared with the original algorithm, it saves one qubit and reduces the complexity with error ϵ from O(1/ϵ2) to O(1/ϵ). Thanks to these optimizations, we can obtain the energy spectrum and ground state of the effective Hamiltonian of the water molecule more accurately and in only 20 percent of the time in a four-qubit processor compared to previous work. More generally, for non-Hermitian matrices, a singular-value decomposition has essential applications in more areas, such as recommendation systems and principal component analysis. The QRT has also been used to prepare singular vectors corresponding to the largest singular values, demonstrating its potential for applications in quantum machine learning.

Funder

National Basic Research Program of China

National Natural Science Foundation of China

National Key Research and Development Program of China

Key Research and Development Program of Guangdong province

Beijing Advanced Innovation Center for Future Chip

Publisher

MDPI AG

Subject

General Physics and Astronomy

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