Limit theorems for quantum walks with memory
Limit theorems for quantum walks with memory
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DOI：
10.26421/qic10.11-12-10
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
N. Konno;T. Machida
中科院分区：
文献类型：
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作者：
N. Konno;T. Machida
最近，Mc Gettrick [1]提出并研究了一维离散二态量子行走。他用路径计数法给出了量子阱振幅的表达式。此外，他还证明了在任何偶数时间，行走的返回概率都大于1/2。在本文中，我们将行走视为无记忆的四态量子阱来计算平稳分布。我们的结果与他的主张是一致的。此外，我们还得到了重标度量子阱的弱极限定理。这种行为与经典的无规行走和通常的无记忆二态量子阱有着显著的不同，正如他的数值模拟所表明的那样。
Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk(QW) with a memory in one dimension. He gave an expression for the amplitude ofthe QW by path counting method. Moreover he showed that the return probability ofthe walk is more than 1/2 for any even time. In this paper, we compute the stationarydistribution by considering the walk as a 4-state QW without memory. Our result isconsistent with his claim. In addition, we obtain the weak limit theorem of the rescaledQW. This behavior is strikingly different from the corresponding classical random walkand the usual 2-state QW without memory as his numerical simulations suggested.