# The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins

## TL;DR

This paper classifies the Witten index for 1D supersymmetric quantum walks with anisotropic coins, revealing its topological significance and similarities to supersymmetric Dirac particles.

## Contribution

It provides a complete classification of the Witten index for one-dimensional split-step quantum walks, linking it to topological and supersymmetric properties.

## Key findings

- Witten index classifies topologically protected states
- Similarity to supersymmetric Dirac particles
- Provides a complete mathematical framework for the index

## Abstract

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.