# One-dimensional quantum walks

@inproceedings{Ambainis2001OnedimensionalQW,
title={One-dimensional quantum walks},
author={Andris Ambainis and Eric Bach and Ashwin Nayak and Ashvin Vishwanath and John Watrous},
booktitle={STOC '01},
year={2001}
}
• Published in STOC '01 6 July 2001
• Mathematics, Physics
We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the <italic>Hadamard walk</italic>. Several striking differences between the quantum and classical cases are observed. For example, when unrestricted in either direction, the Hadamard walk has position that is nearly uniformly distributed in the range <italic>[-t/\sqrt 2, t/\sqrt 2]</italic> after <italic>t…
491 Citations

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