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Ito’s Formula for the Discrete-Time Quantum Walk in Two Dimensions

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DOI: 10.4236/jqis.2012.22008    3,424 Downloads   6,706 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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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