产生一维离散时间量子行走的哈密顿量
The Hamiltonians generating one-dimensional discrete-time quantum walks
摘要：
给出了产生一维离散时间量子行走的哈密顿量的显式公式。利用前面介绍的代数结构推导出了该公式。哈密顿量的平方原来是一个基本上没有“硬币寄存器”的算子，因此它可以与一维连续时间量子行走进行比较。结果表明，在一个参数的限制下，一维连续时间量子行走是由一维离散时间量子行走的哈密顿量所定义的算符得到的，该参数表示定义离散时间量子行走的酉矩阵的对角分量的大小.因此，这一结果可以被视为，在一维，作为一个问题的部分答案所提出的Ambainis。
英文摘要：
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.
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