Pretty good state transfer in discrete-time quantum walks
Ada Chan, Hanmeng Zhan
Abstract
Abstract We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more specifically, the vertices involved in pretty good state transfer must be strongly cospectral relative to this matrix, and the arccosines of its eigenvalues must satisfy some number theoretic conditions. Using normalized adjacency matrices, cyclic covers, and the theory on linear relations between geodetic angles, we construct several infinite families of walks that exhibits this phenomenon.
Topics & Concepts
Quantum walkAdjacency matrixMathematicsEigenvalues and eigenvectorsTransfer matrixGraph energyTransfer (computing)State (computer science)Adjacency listHermitian matrixMatrix (chemical analysis)QuantumDiscrete mathematicsCombinatoricsGraphPure mathematicsQuantum mechanicsPhysicsQuantum algorithmComputer scienceLine graphAlgorithmComposite materialMaterials scienceComputer visionParallel computingGraph powerQuantum Computing Algorithms and ArchitectureQuantum-Dot Cellular AutomataQuantum Information and Cryptography