Optimal Quantum Transfer from Input Flying Qubit to Lossy Memory

A key challenge in a quantum network is to transfer a propagating input qubit to a stationary memory mode. For an uncontrolled transfer, the input qubit faces significant reflection from the memory resonator. A solution can be provided by a resonator with a dynamically tunable rate for coupling internal and external fields. For a given input temporal profile, the coupling rate can be tuned such that the raw resonator output continuously destructively interferes with the immediately reflected input signal, making the overall output field a vacuum state, and thus ensuring that the input is fully absorbed into the resonator. Here, we derive the resonator's optimal output coupling rate profile in the presence of intrinsic loss, employing the scattering-Lindbladian-Hamiltonian (SLH) formalism to model the open quantum system. It is imperative to provide a "seed" internal population, using the initial edge of the input field, in order to subsequently cancel out the reflected input via destructive interference. We derive the time required for this initial stage, showing that the loss due to reflection is small enough that the fidelity remains close to unity. We demonstrate that a net transfer fidelity of 99.9% can be reached given practical input and resonator parameters.