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arXiv · 2009.03618

An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks

Ji Guan·Qisheng Wang·Mingsheng Ying
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Abstract

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.

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Ji Guan, Qisheng Wang, Mingsheng Ying. 2020-09-08. An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks. https://doi.org/10.26421/qic21.5-6-4

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