Yang Fan, Chen Xinyu, Zhao Dafa, Wei Shijie, Wen Jingwei, Wang Hefeng, Xin Tao, Long Guilu
State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
Entropy (Basel). 2022 Dec 28;25(1):61. doi: 10.3390/e25010061.
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.
求解厄米矩阵的本征问题在许多领域都是一个重要问题。量子共振跃迁（QRT）算法已被提出并证明可使用量子设备解决此问题。为了更好地利用近期的量子设备实现QRT的能力，我们改进了该算法并开发了一种新程序以降低时间复杂度。与原始算法相比，它节省了一个量子比特，并将误差为ϵ时的复杂度从O(1/ϵ²)降低到O(1/ϵ)。得益于这些优化，与之前的工作相比，我们可以在一个四量子比特处理器中仅用20%的时间更准确地获得水分子有效哈密顿量的能谱和基态。更一般地，对于非厄米矩阵，奇异值分解在更多领域有着重要应用，如推荐系统和主成分分析。QRT也已被用于制备对应于最大奇异值的奇异向量，展示了其在量子机器学习中的应用潜力。
