The Hamiltonians generating one-dimensional discrete-time quantum walks
| Autor: | Tate, Tatsuya |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Interdisciplinary Information Sciences 19, No. 2 (2013), 149--156 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4036/iis.2013.149 |
| Popis: | An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an operator without, essentially, the `coin register', and hence it can be compared with the one-dimensional continuous-time quantum walk. It is shown that, under a limit with respect to a parameter, which expresses the magnitude of the diagonal components of the unitary matrix defining the discrete-time quantum walks, the one-dimensional continuous-time quantum walk is obtained from operators defined through the Hamiltonians of the one-dimensional discrete-time quantum walks. Thus, this result can be regarded, in one-dimension, as a partial answer to a problem proposed by Ambainis. Comment: 9 pages |
| Databáze: | arXiv |
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