This study investigates the unitary equivalence classes of quantum walks on cycles. We show that unitary equivalence classes of quantum walks on a cycle with N vertices are parameterized by 2N real parameters. Moreover, the ranges of two of the parameters are restricted, and the ranges depend on the parity of N.

中文翻译：

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循环中量子行走的参数化

这项研究调查了循环中量子游动的the等价类。我们证明，具有N个顶点的循环上的量子游动的unit等价类由2 N个实参参数化。此外，两个参数的范围受到限制，并且范围取决于N的奇偶性。