Absorption Probabilities for the Two-Barrier Quantum Walk
Quantum Physics
2010-07-16 v1 Number Theory
Abstract
Let p_j^(n) be the probability that a Hadamard quantum walk, started at site j on the integer lattice {0,...,n}, is absorbed at 0. We give an explicit formula for p_j^(n). Our formula proves a conjecture of John Watrous, concerning an empirically observed linear fractional recurrence relation for the numbers p_1^(n).
Cite
@article{arxiv.0901.4349,
title = {Absorption Probabilities for the Two-Barrier Quantum Walk},
author = {Eric Bach and Lev Borisov},
journal= {arXiv preprint arXiv:0901.4349},
year = {2010}
}
Comments
11 pages