Quantum walks driven by quantum coins with two multiple eigenvalues
Quantum walks driven by quantum coins with two multiple eigenvalues
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DOI：
10.1007/s40509-022-00281-1
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
N. Konno;I. Sato;E. Segawa;Yutaka Shikano
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文献类型：
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作者：
N. Konno;I. Sato;E. Segawa;Yutaka Shikano
本文考虑了图上具有局部硬币算子和触发器移位的量子行走的谱分析。量子币算符通常有两个不同的本征值，对任意的，其中G的最小次数为。我们表明，这种量子行走可以分解成一个元胞自动机上的时间演化描述的自伴算子T和它的余数。我们得到了T的本征值及其本征空间如何提升为原量子行走的本征值及其本征空间。作为应用，我们在Fourier空间中用移动表示了Grover行走的特征多项式.
We consider a spectral analysis on the quantum walks on graphwith the local coin operatorsand the flip flop shift. The quantum coin operators have commonly two distinct eigenvaluesandfor anywith, whereis the minimum degrees ofG. We show that this quantum walk can be decomposed into a cellular automaton onwhose time evolution is described by a self adjoint operatorTand its remainder. We obtain how the eigenvalues and its eigenspace ofTare lifted up to as those of the original quantum walk. As an application, we express the eigenpolynomial of the Grover walk onwith the moving shift in the Fourier space.