Ito’s Formula for the Discrete-Time Quantum Walk in Two Dimensions
Clement Ampadu
31 Carrolton Road, Boston, USA.
DOI: 10.4236/jqis.2012.22008   PDF    HTML     3,969 Downloads   7,695 Views   Citations

Abstract

Following Konno [1], it is natural to ask: What is the Ito’s formula for the discrete time quantum walk on a graph different than Z, the set of integers? In this paper we answer the question for the discrete time quantum walk on Z2, the square lattice.

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C. Ampadu, "Ito’s Formula for the Discrete-Time Quantum Walk in Two Dimensions," Journal of Quantum Information Science, Vol. 2 No. 2, 2012, pp. 41-47. doi: 10.4236/jqis.2012.22008.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] N. Konno, “A Note on Ito’s Formula for Discrete-Time Quantum Walk,” Cornell University Library, New York, 2011.
[2] T. Fujita, “Stochastic Calculus for Finance (in Japanese),” Kodansha, Tokyo, 2002.
[3] T. Fujita, “Random Walks and Stochastic Calculus (in Japanese),” Nippon-Hyoron-Sha Co. Ltd., Tokyo, 2008.
[4] C. Ampadu, “Sojourn Times for the One Dimensional Grover Walk,” Cornell University Library, New York, 2011.

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