Controlled preparation and unconditional transport on a fluctuating quantum graph

arXiv:2611.14588v1 Announce Type: new Abstract: Lieb--Robinson bounds limit the spread of quantum information, but do not establish that a prescribed input can be prepared and transmitted with appreciable probability. For quantum graphs with fluctuating edges, connecting spectral propagation to unconditional readout also requires control of graph coherence, finite boundaries, and preparation errors. We address this problem in a one-probe model on a prescribed square candidate lattice, combining a generalized Rokhsar--Kivelson parent, spectral reduction, adiabatic preparation, and local dynamical estimates. Assuming a supplied coherent graph ground state, we construct a finite-source wave packet and a hopping ramp that populate an isolated branch with strictly positive group velocity.