Quantum error correction well below the color code threshold
Abstract
Quantum error correction enables scalable fault-tolerant quantum computation by suppressing logical errors exponentially with code distance once physical error rates fall below a critical threshold. Here we demonstrate below-threshold operation of triangular color codes with distances d=3,5, and $7$ on Quantinuum's Helios trapped-ion quantum processor. Leveraging both circuit- and hardware- level leakage reduction schemes, we achieve logical error rates as low as 5−2+4× 10−6, and demonstrate error suppression by over an order of magnitude, Λ=12−2+3, with each successive increase in code distance. Moreover, we demonstrate below threshold scaling of error rates for Clifford two-qubit randomized benchmarking circuits when encoded in d=3,5 color codes, achieving logical error rate of 7+3−3× 10−5 per logical two-qubit Clifford at distance $5$ with a suppression factor of Λ=9−3+8. We compare logical performance for existing near-optimal algorithmic decoders, and both convolutional neural network and transformer-based neural network decoders capable of real-time decoding an order of magnitude faster than the syndrome extraction rate. These results approach the logical error rates required for megaquop-scale quantum computation and indicate that scaled trapped-ion processors could reach application-relevant performance with substantially smaller code blocks than indicated by previous results in other qubit modalities.
Related
- Ensemble Dependence of the Critical Exponent at a Quantum Error Correction Threshold
- Entropy threshold: A simple proxy for performance of quantum error correction
- Below-threshold execution of fault-tolerant ripple-carry addition on a trapped-ion quantum computer
- Bosonic quantum error correction with microwave cavities for quantum repeaters
- Error-Correction Transitions in Finite-Depth Quantum Channels
BibTeX
@misc{lavasani2026quantum,
title = {{Quantum error correction well below the color code threshold}},
author = {Ali Lavasani and Adam P. Reed and Joan M. Dreiling and Annie J. Park and Michael Mills and Matteo Puviani and Gabriel Matos and M. S. Allman and Noah Berthusen and Natalie C. Brown and Victor E. Colussi and Brian Estey and Cameron Foltz and Daniel Gresh and Reza Haghshenas and Akhil Isanaka and Nikhil Kotibhaskar and Anthony Ransford and Ciarán Ryan-Anderson and Brian Neyenhuis and David Hayes and Tzvetan S. Metodi and Andrew C. Potter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24077},
eprint = {2610.24077},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24077},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum error correction well below the color code threshold
AU - Ali Lavasani
AU - Adam P. Reed
AU - Joan M. Dreiling
AU - Annie J. Park
AU - Michael Mills
AU - Matteo Puviani
AU - Gabriel Matos
AU - M. S. Allman
AU - Noah Berthusen
AU - Natalie C. Brown
AU - Victor E. Colussi
AU - Brian Estey
AU - Cameron Foltz
AU - Daniel Gresh
AU - Reza Haghshenas
AU - Akhil Isanaka
AU - Nikhil Kotibhaskar
AU - Anthony Ransford
AU - Ciarán Ryan-Anderson
AU - Brian Neyenhuis
AU - David Hayes
AU - Tzvetan S. Metodi
AU - Andrew C. Potter
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24077
UR - https://arxiv.org/abs/2610.24077
AB - Quantum error correction enables scalable fault-tolerant quantum computation by suppressing logical errors exponentially with code distance once physical error rates fall below a critical threshold. Here we demonstrate below-threshold operation of triangular color codes with distances d=3,5, and $7$ on Quantinuum's Helios trapped-ion quantum processor. Leveraging both circuit- and hardware- level leakage reduction schemes, we achieve logical error rates as low as 5_−2^+4× 10^−6, and demonstrate error suppression by over an order of magnitude, Λ=12_−2^+3, with each successive increase in code distance. Moreover, we demonstrate below threshold scaling of error rates for Clifford two-qubit randomized benchmarking circuits when encoded in d=3,5 color codes, achieving logical error rate of 7^+3_−3× 10^−5 per logical two-qubit Clifford at distance $5$ with a suppression factor of Λ=9_−3^+8. We compare logical performance for existing near-optimal algorithmic decoders, and both convolutional neural network and transformer-based neural network decoders capable of real-time decoding an order of magnitude faster than the syndrome extraction rate. These results approach the logical error rates required for megaquop-scale quantum computation and indicate that scaled trapped-ion processors could reach application-relevant performance with substantially smaller code blocks than indicated by previous results in other qubit modalities.
ER -