An index theorem for split-step quantum walks

DOI10.1007/S11128-020-02720-7OpenAlexW3039704464MaRDI QIDQ2681566

Yasumichi Matsuzawa

Publication date: 3 February 2023

Published in: Quantum Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.05061

zbMATH Keywords

winding numbersupersymmetrychiral symmetryindex theoremWitten indexquantum walksFredholm index

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) (Semi-) Fredholm operators; index theories (47A53) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (7)

Asymptotic stability of small bound state of nonlinear quantum walks ⋮ A constructive approach to topological invariants for one-dimensional strictly local operators ⋮ Index theory of chiral unitaries and split-step quantum walks ⋮ An index theorem for one-dimensional gapless non-unitary quantum walks ⋮ The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition ⋮ Spectral mapping theorem of an abstract non-unitary quantum walk ⋮ Unitary equivalence classes of split-step quantum walks

Cites Work

• Unnamed Item
• Generator of an abstract quantum walk
• Quantum walks with an anisotropic coin. I: Spectral theory
• The topological classification of one-dimensional symmetric quantum walks
• The CGMV method for quantum walks
• Supersymmetry for chiral symmetric quantum walks
• The Witten index for 1D supersymmetric quantum walks with anisotropic coins
• ONE-DIMENSIONAL QUANTUM WALKS WITH ONE DEFECT
• Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
• Weak limit theorem for a one-dimensional split-step quantum walk
• Notes on Inhomogeneous Quantum Walks

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