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Hierarchical Generation and Design of Tree-Codes for Resource-Efficient Loss-Tolerant Quantum Communications

Francesco Cesa1,2,3,4,*,†, Tommaso Feri1,2,*,‡, and Angelo Bassi1,2

  • *These authors contributed equally to this work.
  • †Contact author: francesco.cesa@phd.units.it
  • ‡Contact author: tommaso.feri@phd.units.it
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PRX Quantum 7, 020346 – Published 4 June, 2026

DOI: https://doi.org/10.1103/1r46-y9lc

Abstract

We develop protocols for generating loss-tolerant quantum tree-codes; these are designed to safeguard information against qubit losses, with wide applications in quantum communications. Contrary to previous proposals, our method enables top-to-bottom fast encoding and decoding, thereby reducing losses due to the lagging and photon-reordering at the repeater stations. At the hardware level, we show how to achieve this with a single quantum emitter equipped with a static feedback mechanism, which we leverage to engineer entangling gates between a fed-back qubit and multiple emitted qubits in parallel. In addition, analyzing typical patterns within the error-correction decoding graphs, we find optimizations of the structure of tree-codes, which enable improved performance by also reducing the code size; these are based on the introduction of asymmetries in the code, which mimic the intrinsic adaptiveness of the recovery procedure. We show numerically that these improvements together significantly enhance the loss-correction performance. Specifically, focusing on quantum repeater protocols, we show that our fast recovery scheme (decoding-encoding) allows for improved repeater rates with smaller photon numbers per code.

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Popular Summary

Photon loss constitutes a major roadblock for sending quantum information over long distances, as the loss probability grows exponentially in the transmission distance. Such an effect, in principle, can be overcome via quantum error-correction schemes specialized against loss errors, which leverage entanglement to protect the information.

This work introduces a new method to generate the needed entangled photonic states with simple quantum-optical tools. In this protocol, the state is generated “top-to-bottom,” which enables to shorten the time vulnerable photons must wait before errors are corrected, cutting additional losses that appear in practical repeaters. In addition, a new code design is presented based on the introduction of asymmetries that mimic the error-correction procedure: this allows to further boost the effectiveness of the repeater scheme while using fewer photons.

Together, these improvements raise predicted quantum repeater rates and reduce hardware demands, helping bring long-distance, loss-tolerant quantum communication closer to near-term devices.

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PRX Quantum 7, 020346– Published 4 June, 2026
  • Received 28 March 2025
  • Revised 10 November 2025
  • Accepted 9 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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