Quantum Probability Current Guided Reduction of Coupling Control Degrees of Freedom for Excitation Transport
Time-dependent coherent control can enhance excitation transport in open quantum networks, but independently controlling every inter-site coupling creates a control space of high dimension and leads to difficult optimization problems. We introduce an edge-ranking strategy based on the control-induced change in the gradient component of the time-integrated quantum probability current, which is obtained via a graph Hodge decomposition. When our strategy is applied to the seven-site Fenna-Matthews-Olson (FMO) model, the six-edge set retains $99.83\%$ of the enhancement achieved by full control, and the four-edge set retains $97.60\%$ while reducing the pulse fluence---used here as a proxy for control effort---by $41.55\%$ relative to full control. Dephasing scans and comparisons with random edge sets and random networks provide numerical support for the relevance and potential broader utility of the ranking. These results show that edge selection guided by the quantum probability current can substantially reduce the control space while preserving high transport performance with lower control effort.