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

• URL: http://arxiv.org/abs/2009.03618v2
• Date: Sat, 27 Mar 2021 07:40:31 GMT
• Title: An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks
• Authors: Ji Guan, Qisheng Wang and Mingsheng Ying
• Abstract summary: 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. 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.
• Score: 3.068108039722565
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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