Unitary equivalence classes of split-step quantum walks

Abstract

This study investigates the unitary equivalence of split-step quantum walks (SSQW). We consider a new class of quantum walks which includes all SSQWs. We show the explicit form of quantum walks in this class, and clarify their unitary equivalence classes. Unitary equivalence classes of Suzuki's SSQW are also given.

18 pages

References in corpus (5)

• Exploring Topological Phases With Quantum Walks
• The topological classification of one-dimensional symmetric quantum walks
• Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
• Unitary Equivalence of Quantum Walks
• The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins

Cited by in corpus (2)

• A novel approach for quantum financial simulation and quantum state preparation
• The bulk-edge correspondence for the split-step quantum walk on the one-dimensional integer lattice