Long-Distance End-to-End Quantum State Transfer in a Transmon Qubit Network Connected Via Optical Photons

An essential aspect of a quantum internet is the transfer of qubits between different physical modes. Transmon qubits excel in computation, long-decoherence-time phonons are suitable for storing qubits, and optical photons are efficient for long-distance communication. Therefore, an ideal quantum network will be based on hybrid physical platforms. We present an efficient protocol for quantum state transfer between two transmon qubits at the end nodes, connected by an optical channel, piezoelectric RF-photon/phonon qubit converters, and optomechanical phonon/photon transducers. Starting with a qubit initially encoded in a transmon, we theoretically study the sequential transduction of the qubit to transient microwave photon, microwave phonon, and optical photon modes, followed by the inverse of those processes to convert the qubit back to transmon encoding in the other end node. We derive the optimal time profiles for the system's tunable parameters in the presence of intrinsic losses, using the scattering-Lindbladian-Hamiltonian (SLH) formalism to model the open quantum subsystems. For a practical system, a fidelity of 92.2 to 92.7% in the limit of a lossless optical fiber is attainable.