  In a quantum network, a key challenge is to minimize the direct reflection of
flying qubits as they couple to stationary, resonator-based memory qubits, as
the reflected amplitude represents state transfer infidelity that cannot be
directly recovered. Optimizing the transfer fidelity can be accomplished by
dynamically varying the resonator's coupling rate to the flying qubit field.
Here, we analytically derive the optimal coupling rate profile in the presence
of intrinsic loss of the quantum memory using an open quantum systems method
that can account for intrinsic resonator losses. We show that, since the
resonator field must be initially empty, an initial amplitude in the resonator
must be generated in order to cancel reflections via destructive interference;
moreover, we show that this initial amplitude can be made sufficiently small as
to allow the net infidelity throughout the complete transfer process to be
close to unity. We then derive the time-varying resonator coupling that
maximizes the state transfer fidelity as a function of the initial population
and intrinsic loss rate, providing a complete protocol for optimal quantum
state transfer between the flying qubit and resonator qubit. We present
analytical expressions and numerical examples of the fidelities for the
complete protocol using exponential and Gaussian profiles. We show that a state
transfer fidelity of around 99.9% can be reached for practical intrinsic losses
of resonators used as quantum memories.
