论文标题
用于计算量子随机步行概率的基于HHL的算法
An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks
论文作者
论文摘要
我们提出了HHL（Harrow-Hassidim-Lloyd）算法的新应用 - 一种线性方程式的量子算法求解系统 - 在解决有关量子随机步行的开放问题，即计算一般（不仅是Hadamard）一维量子量界的量子击中（或吸收）概率（或吸收）概率。这是通过一个简单的观察结果来实现的，即计算量子随机步行概率的问题可以降低为反转矩阵。然后开发了具有HHL算法作为子例程的量子算法用于解决该问题，该问题比通过数值实验比已知的经典算法更快。
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm -- a quantum algorithm solving systems of linear equations -- in solving an open problem about quantum random walks, namely computing hitting (or absorption) probabilities of a general (not only Hadamard) one-dimensional quantum random walks with two absorbing boundaries. This is achieved by a simple observation that the problem of computing hitting probabilities of quantum random walks can be reduced to inverting a matrix. Then a quantum algorithm with the HHL algorithm as a subroutine is developed for solving the problem, which is faster than the known classical algorithms by numerical experiments.
