  Quantum walks have attracted attention as a promising platform realizing
topological phenomena and many physicists have introduced various types of
indices to characterize topologically protected bound states that are robust
against perturbations. In this paper, we introduce an index from a
supersymmetric point of view. This allows us to define indices for all chiral
symmetric quantum walks such as multi-dimensional split-step quantum walks and
quantum walks on graphs, for which there has been no index theory. Moreover,
the index gives a lower bound on the number of bound states robust against
compact perturbations. We also calculate the index for several concrete
examples including the unitary transformation that appears in Grover's search
algorithm.
