Strong dispersion property for the quantum walk on the hypercube
| Autor: | Kokainis, Martins, Prūsis, Krišjānis, Vihrovs, Jevgēnijs, Kashcheyevs, Vyacheslavs, Ambainis, Andris |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 55 495301 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/aca6b9 |
| Popis: | We show that the discrete time quantum walk on the Boolean hypercube of dimension $n$ has a strong dispersion property: if the walk is started in one vertex, then the probability of the walker being at any particular vertex after $O(n)$ steps is of an order $O(1.4818^{-n})$. This improves over the known mixing results for this quantum walk which show that the probability distribution after $O(n)$ steps is close to uniform but do not show that the probability is small for every vertex. A rigorous proof of this result involves an intricate argument about analytic properties of Bessel functions. Comment: 27 pages, 4 figures |
| Databáze: | arXiv |
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