Li Xinying, Zheng Pei-Lin, Pan Chengkang, Wang Fei, Cui Chunfeng, Lu Xian
China Mobile Research Institute, Beijing, 100053, China.
Sci Rep. 2025 Aug 5;15(1):28559. doi: 10.1038/s41598-025-13092-2.
Matrix operations are crucial to various computational tasks in various fields, and quantum computing offers a promising avenue to accelerate these operations. We present a quantum matrix multiplication (QMM) algorithm that employs amplitude encoding and combines quantum walks with Chebyshev polynomial approximation to achieve quadratic acceleration for matrix chain multiplication where the same matrix is applied K times while maintaining logarithmic complexity in matrix dimension and precision. The algorithm can be applied to any complex matrix. Furthermore, we discuss integrating our QMM algorithm as a subroutine in other matrix operations and propose strategies to optimize QMM for matrices with large condition numbers with numerical simulation.
矩阵运算对于各个领域的各种计算任务都至关重要，而量子计算为加速这些运算提供了一条很有前景的途径。我们提出了一种量子矩阵乘法（QMM）算法，该算法采用幅度编码，并将量子游走与切比雪夫多项式逼近相结合，以实现矩阵链乘法的二次加速，其中同一个矩阵被应用K次，同时在矩阵维度和精度方面保持对数复杂度。该算法可应用于任何复矩阵。此外，我们讨论了将我们的QMM算法作为子例程集成到其他矩阵运算中，并通过数值模拟提出了针对具有大条件数的矩阵优化QMM的策略。
