  The qubit scalability imposes a paramount challenge in the field of quantum
computing. Photonic interconnects between distinct quantum computing modules
provide a solution to deal with this issue. The fundamental part of this
approach is entanglement distribution via travelling photons emitted by matter
qubits. However, randomness of the spontaneous emission in the matter qubits
limits both the entanglement fidelity and the generation rate. In this paper,
by numerical and analytical methods, we investigate the relationship between
the entanglement affected by the spontaneous emission and the waveform of the
pump pulse used in the photon generation. We confirm and analyze a
rate-fidelity trade-off in the entanglement swapping with Gaussian pump pulses
and show that a simple extension to non-Gaussian pump pulses improves the
trade-off in a certain parameter region. Furthermore we extend our analysis to
entanglement distribution in the general multipartite setting and show that the
analysis of the bipartite entanglement can be straightforwardly applied in this
case as well.
