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