  Chirally symmetric discrete-time quantum walks possess supersymmetry, and
their Witten indices can be naturally defined. The Witten index gives a lower
bound for the number of topologically protected bound states. The purpose of
this paper is to give a complete classification of the Witten index associated
with a one-dimensional split-step quantum walk. It turns out that the Witten
index of this model exhibits striking similarity to the one associated with a
Dirac particle in supersymmetric quantum mechanics.
