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Entanglement distribution is a core mechanism for the future quantumInternet. The quantum world is, however, a faulty environment. Hence,successful entanglement swapping is error-prone. The occurrence of quantumstate errors can be mitigated using purification and error correction, whichcan be repeated in the former case and concatenated in the latter case.Repeated purification merges low-fidelity qubits into higher-quality ones,while concatenated error correction builds upon the redundancy of quantuminformation. In this article, we study in-depth and compare the two options:repeated purification and concatenated error correction. We consider usingrepeated purification and concatenated error correction to mitigate thepresence of faults that occur during the establishment of Bell pairs betweenremote network nodes. We compare their performance versus the number ofrepetitions or concatenations, to reach a certain level of fidelity in quantumnetworks. We study their resource requirements, namely, their work memorycomplexity (e.g., number of stored qubits) and operational complexity (e.g.,number of operations). Our analysis demonstrates that concatenated errorcorrection, versus repeated purification, requires fewer iterations and haslower operational complexity than repeated purification to reach high fidelityat the expense of increased memory requirements.

Repeated Purification versus Concatenated Error Correction in Fault Tolerant Quantum Networks