Journal
QUANTUM INFORMATION PROCESSING
Volume 1, Issue 5, Pages 345-354Publisher
SPRINGER
DOI: 10.1023/A:1023413713008
Keywords
Quantum random walk; the Hadamard walk; limit theorems
Funding
- Japan Society of the Promotion of Science [12440024]
- Grants-in-Aid for Scientific Research [12440024] Funding Source: KAKEN
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This letter treats the quantum random walk on the line determined by a 2 x 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state phi is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.
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