An index theorem for split-step quantum walks

2019/03/12 by Yasumichi Matsuzawa, Matsuzawa, Yasumichi
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.1903.05061

openalex publication_date 2019/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Weak limit theorem for a one-dimensional split-step quantum walk

Related

• Supersymmetric quantum walks with chiral symmetry
• Spectral Analysis of Non-unitary Two-phase Quantum Walks in One Dimension
• The bulk-edge correspondence for the split-step quantum walk on the one-dimensional integer lattice
• Unitary equivalence classes of split-step quantum walks
• Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic Parameters