Split-step quantum walks are models of supersymmetric quantum walk, and thus, their Witten indices can be defined. We prove that the Witten index of a split-step quantum walk coincides with the difference between the winding numbers of functions corresponding to the right limit of coins and the left limit of coins. As a corollary, we give an alternative derivation of the index formula for split-step quantum walks, which is recently obtained by Suzuki and Tanaka.

中文翻译：

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分步量子行走的指数定理

分步量子游走是超对称量子游走的模型，因此可以定义其Witten指数。我们证明了分步式量子行走的维滕指数与对应于硬币的右极限和硬币的左极限的函数的绕数之差一致。作为推论，我们给出了分步式量子行走的指数公式的另一种推导，该公式最近由Suzuki和Tanaka获得。