Quantum walk Eigen-value 2 Eigenvalues and eigenfunctions 2 Adjoint matrix 1 Asymptotic stability 1 Bound states 1 Bound-states 1 Coherent superpositions 1 Evolution operator 1 Flexible electronics 1 Graph theory 1 Long time behavior 1 Mapping theorem 1 Multi-bits 1 Nonlocalities 1 Of quantum-information 1 Photomapping 1 Position dependents 1 Quantum chemistry 1 Quantum computers 1 Quantum information applications 1 Quantum optics 1 Quantum theory 1 Quantum walks 1 Random Numbers 1 Random number generation 1 Rich dynamics 1 Scattering waves 1 Shift operators 1 Spectral graph theory 1