Topological State Transfer through Effective Boundary-Mode Channels

Abstract Localized edge modes provide a compact channel for transferring an excitation through an extended lattice, but the relation between the microscopic chain and the few levels that actually govern the transfer is often left implicit. We develop this boundary-subspace description for a superconducting-qubit realization of the Rice–Mele model in the single-excitation sector. For one finite chain, projection onto the two edge modes yields a Landau–Zener Hamiltonian whose detuning and hybridization identify the adiabatic transfer path and the spectral constraint relevant to protocol optimization. We then join two Rice–Mele segments at a single physical boundary qubit. The resulting three localized modes form an effective three-state channel with microscopically determined, independently tunable energies and couplings. This channel supports both a zero-energy dark-state passage and an open Rice–Mele-type passage driven by time-dependent bonds and onsite potentials. Direct simulations of the complete qubit chains reproduce the effective-channel dynamics. Under matched control bounds, dividing the transport distance at a shared boundary also preserves larger finite-size edge-mode couplings and reaches a stable high-fidelity regime faster than transfer through one uninterrupted chain. The boundary-mode projection thus relates the microscopic controls directly to the effective energies, finite-size couplings, and adiabatic gaps that govern the transfer.