Interoperability in encoded quantum repeater networks

TL;DR

This paper analyzes methods for creating heterogeneously encoded Bell pairs in quantum repeater networks, focusing on error correction, protocol efficiency, and fidelity under realistic error models.

Contribution

It introduces a generalized procedure for encoding Bell pairs between different quantum error correcting codes and compares three protocols for their efficiency and fidelity.

Findings

Postselected protocol performs best in fidelity and resource efficiency.

High-fidelity logical Bell pairs achievable with local gate error rate of 10^-3.

Monte Carlo simulations evaluate error probabilities across different codes.

Abstract

The future of quantum repeater networking will require interoperability between various error correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in the context of quantum networking has been performed. In this paper, we analyze a generalized procedure to create Bell pairs encoded heterogeneously between two separate codes used often in error corrected quantum repeater network designs. We begin with a physical Bell pair, then encode each qubit in a different error correcting code, using entanglement purification to increase the fidelity. We investigate three separate protocols for preparing the purified encoded Bell pair. We calculate the error probability of those schemes between the Steane [[7,1,3]] code, a distance three surface code and single physical qubits by Monte Carlo simulation under a standard Pauli error model, and estimate the resource efficiency of the procedures. A local gate error rate of $10^{-3}$ allows us to create high-fidelity logical Bell pairs between any of our chosen codes. We find that a postselected model, where any detected parity flips in code stabilizers result in a restart of the protocol, performs the best.