# Repeated Purification versus Concatenated Error Correction in Fault Tolerant Quantum Networks

## TL;DR

This paper compares repeated purification and concatenated error correction for improving entanglement fidelity in quantum networks, analyzing their resource requirements and operational efficiencies.

## Contribution

It provides an in-depth comparison of two quantum error mitigation strategies, highlighting their performance trade-offs in quantum network entanglement distribution.

## Key findings

- Concatenated error correction requires fewer iterations than repeated purification.
- Concatenated error correction has lower operational complexity.
- It demands more memory resources than repeated purification.

## Abstract

Entanglement distribution is a core mechanism for the future quantum Internet. The quantum world is, however, a faulty environment. Hence, successful entanglement swapping is error-prone. The occurrence of quantum state errors can be mitigated using purification and error correction, which can 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 quantum information. In this article, we study in-depth and compare the two options: repeated purification and concatenated error correction. We consider using repeated purification and concatenated error correction to mitigate the presence of faults that occur during the establishment of Bell pairs between remote network nodes. We compare their performance versus the number of repetitions or concatenations, to reach a certain level of fidelity in quantum networks. We study their resource requirements, namely, their work memory complexity (e.g., number of stored qubits) and operational complexity (e.g., number of operations). Our analysis demonstrates that concatenated error correction, versus repeated purification, requires fewer iterations and has lower operational complexity than repeated purification to reach high fidelity at the expense of increased memory requirements.