Dispersive topological bound states in the continuum for controllable quantum-state transport in three-state discrete-time quantum walks

We show that a three-state discrete-time quantum walk (DTQW) on a square lattice, with an SU(3) coin, realizes stroboscopic Floquet phases that host dispersive topological bound states in the continuum (TBICs). Time-independent step operations act as the periodic drive and map the one-step unitary to an effective Floquet Hamiltonian. Chern-number calculations resolve three quasienergy bands and their phase boundaries as the rotation angles are varied, and bulk-boundary correspondence in semi-infinite and fully finite geometries accounts for the edge spectra. At interfaces between media with the same bandwise Chern numbers but different coin parameters, nonchiral edge modes become embedded yet localized TBICs with tunable group velocity and selective excitation, while numerics indicate robustness to moderate coin disorder. Together with feasible routes in trapped-ion, cold-atom, and photonic platforms and an explicit decoherence model, these results identify DTQWs as a controllable setting for protected quantum-state transport and storage, relevant to quantum information and communication technologies.