Unitary equivalence classes of split-step quantum walks

In this study, we investigate the unitary equivalence of split-step quantum walks (SSQWs). Introduced by Kitagawa and generalized Suzuki, SSQWs are two-state discrete-time on a one-dimensional lattice. work, define new class that includes all making use rank conditions, which state (1) operators representing walk from vertex x to $$x\pm 1$$ is less than or equal 1 (2) (i.e., itself) 2. Initially, abstractly in class, then clarify presenting explicit form such walks. We also calculate their classes show four real parameters required for each parameterize classes. Further, consider Suzuki’s prove can be real. Finally, discuss chiral symmetry SSQWs.