Abstract
Long-distance quantum communication requires architectures that withstand photon loss and operational noise without relying on two-way classical signalling that incurs round-trip latency. Motivated by recent hybrid designs combining photonic trees with small stabilizer codes, we benchmark the Steane code [[7, 1, 3]] against the standard five-qubit [[5, 1, 3]] baseline within a tree-assisted repeater architecture. Unlike the saturated five-qubit code, which is constrained by a fully populated syndrome space, our implementation exploits the Steane code’s underpopulated syndrome space to correct all single-qubit erasures and additionally a subset of two-qubit errors. Consequently, the Steane code demonstrates superior robustness at realistic re-encoding error rates (
$$backslashepsilon _rbackslashge 0.05backslash%$$), maintaining higher message qubit transmission success rates than the baseline. Notably, at
$$backslashepsilon _r=0.2backslash%$$, the Steane-based repeater maintains a competitive cost threshold up to 5000 km, significantly exceeding the 800 km limit of the five-qubit code. These results suggest that the Steane code’s capacity for erasure correction offers a practical advantage for one-way repeaters, outweighing the overhead of its larger block size.
Citation
BibTeX
@article{J029,
abstract = {Long-distance quantum communication requires architectures that withstand photon loss and operational noise without relying on two-way classical signalling that incurs round-trip latency. Motivated by recent hybrid designs combining photonic trees with small stabilizer codes, we benchmark the Steane code [[7, 1, 3]] against the standard five-qubit [[5, 1, 3]] baseline within a tree-assisted repeater architecture. Unlike the saturated five-qubit code, which is constrained by a fully populated syndrome space, our implementation exploits the Steane code's underpopulated syndrome space to correct all single-qubit erasures and additionally a subset of two-qubit errors. Consequently, the Steane code demonstrates superior robustness at realistic re-encoding error rates (\$\$\backslashepsilon _\r\\backslashge 0.05\backslash%\$\$), maintaining higher message qubit transmission success rates than the baseline. Notably, at \$\$\backslashepsilon _\r\=0.2\backslash%\$\$, the Steane-based repeater maintains a competitive cost threshold up to 5000 km, significantly exceeding the 800 km limit of the five-qubit code. These results suggest that the Steane code's capacity for erasure correction offers a practical advantage for one-way repeaters, outweighing the overhead of its larger block size.},
author = {Bihan, Subhan Zawad
and Choudhury, Anindya Kishore
and me},
citationnos = {0},
citesurl = {https://scholar.google.com/citations?view_op=view_citation&hl=en&user=Fu8Hkb4AAAAJ&sortby=pubdate&citation_for_view=Fu8Hkb4AAAAJ:08ZZubdj9fEC},
day = {28},
doi = {10.1007/s11128-026-05327-6},
issn = {1573-1332},
journal = {Quantum Information Processing},
month = {8},
number = {9},
pages = {301},
sjr = {Q2},
title = {Steane $[[7,1,3]]$ outer coding for loss-tolerant one-way quantum repeaters},
url = {https://doi.org/10.1007/s11128-026-05327-6},
volume = {25},
year = {2026}
}