An index theorem for one-dimensional gapless non-unitary quantum walks

DOI10.1007/s11128-021-03212-yOpenAlexW3198545894MaRDI QIDQ2685578

Daiju Funakawa, Keisuke Asahara, Motoki Seki, Yohei Tanaka

Publication date: 22 February 2023

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

Full work available at URL: https://doi.org/10.1007/s11128-021-03212-y

zbMATH Keywords

supersymmetrychiral symmetryWitten indexgapless quantum walksnon-unitary quantum walks

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (Semi-) Fredholm operators; index theories (47A53) Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) (81T35)

Related Items (2)

Index theory of chiral unitaries and split-step quantum walks ⋮ Spectral mapping theorem of an abstract non-unitary quantum walk

Uses Software

• Split Step Explorer

Cites Work

• Unnamed Item
• Asymptotic velocity of a position-dependent quantum walk
• Generator of an abstract quantum walk
• Essential spectrum of the discrete Laplacian on a perturbed periodic graph
• Localization of an inhomogeneous discrete-time quantum walk on the line
• Scattering and inverse scattering for nonlinear quantum walks
• Quantum walks with an anisotropic coin. I: Spectral theory
• Localization of a multi-dimensional quantum walk with one defect
• The topological classification of one-dimensional symmetric quantum walks
• Quantum walks with an anisotropic coin. II: Scattering theory
• Topological phenomena in quantum walks: elementary introduction to the physics of topological phases
• Weak limit theorem for a nonlinear quantum walk
• Unitary equivalence classes of split-step quantum walks
• Time operators for quantum walks
• Chiral Floquet systems and quantum walks at half-period
• Quantum random walks in one dimension
• A constructive approach to topological invariants for one-dimensional strictly local operators
• Supersymmetry for chiral symmetric quantum walks
• The Witten index for 1D supersymmetric quantum walks with anisotropic coins
• A weak limit theorem for a class of long-range-type quantum walks in 1d
• Spectral mapping theorem of an abstract quantum walk
• An index theorem for split-step quantum walks
• ONE-DIMENSIONAL QUANTUM WALKS WITH ONE DEFECT
• Bulk-edge correspondence of one-dimensional quantum walks
• Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
• Analysis on Fock Spaces and Mathematical Theory of Quantum Fields
• QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
• Continuous limits of linear and nonlinear quantum walks
• One-dimensional quantum walks
• Quantum walks on graphs
• Weak limit theorem for a one-dimensional split-step quantum walk
• Nonlinear Dirac Equation
• Quantum time delay for unitary operators: General theory
• Generalized eigenfunctions and scattering matrices for position-dependent quantum walks

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