  We present a quantum repeater protocol for distributing entanglement over
long distances, where each repeater node contains several qubits that can
couple to one single-photon emitter. Photons from the emitters perform heralded
entanglement generation between qubits in neighboring nodes. The protocol
leaves the emitters disentangled from the qubits and photons, thus allowing
them to be reused to entangle other qubits. The protocol can therefore be time
multiplexed, which increases the rate of generated EPR pairs. Deterministic
entanglement swapping and heralded entanglement purification are used to extend
the distance of the entanglement and reduce the error of the entangled qubits,
respectively. We perform a complete protocol analysis by considering all
relevant error sources, such as initialization, two-qubit gate, and qubit
measurement errors, as well as the exponential decoherence of the qubits with
time. The latter is particularly important since we analyze the protocol
performance for a broad range of experimental parameters and obtain secret key
rates ranging from $1 \rightarrow 1000$ Hz at a distance of $1000$ km. Our
results suggest that it is important to reach a qubit memory coherence time of
around one second, and two-qubit gate and measurement errors in the order of
$10^{-3}$ to obtain reasonable secret key rates over distances longer than
achievable with direct transmission.
