UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2022-07-01 17:20

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Conference: Bucharest University Faculty of Physics 2019 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
Classical versus quantum random walk


Authors:
Alexandru DANESC (1), Iulia GHIU (1)


Affiliation:
1) University of Bucharest, Faculty of Physics, P.O. Box MG-11, Bucharest-Magurele, Romania


E-mail
danesc.alexandru@yahoo.com


Keywords:
random walk, quantum walk


Abstract:
In this work we present a comparison between the classical random walk and its generalization to the quantum case. Classical random walk in dimension one, namely the walk which takes place on a line and on a circle, is investigated in detail. We explain the properties of the random walk, by evaluating the probability to end up in the position 'j' after 'n' steps are considered. Further, in the quantum random walk, one has to define two unitary operators: the coin operator and the translational shift operator. The coin operator applies on the spin-1/2 basis and determines the motion of the walk. At a given moment, the quantum walker is in a superposition of different states. One has to perform a measurement on the position in order to extract information regarding the walker. We compute the probability distribution after 'n' steps for the quantum walk.


References:

[1] J. Kempe, Contemporary Physics, 44, 307 (2003).

[2] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.

[3] D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani, Proceedings of the 33th STOC (New York, NY: ACM), pp. 50 – 59 (2001).