Year: 2026
Type: preprint
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 $5_{-2}^{+4}\times 10^{-6}$, 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 $7^{+3}_{-3}\times 10^{-5}$ 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.
Source: arXiv (Cornell University)
Authors: Lavasani, Ali, Reed, Adam P., Dreiling, Joan M., Park, Annie J., Mills, Michael, Puviani, Matteo, Matos, Gabriel, Allman, M. S., Berthusen, Noah, Brown, Natalie C., Colussi, Victor E., Estey, Brian, Foltz, Cameron, Gresh, Daniel, Haghshenas, Reza, Isanaka, Akhil, Kotibhaskar, Nikhil, Ransford, Anthony, Ryan-Anderson, Ciarán, Neyenhuis, Brian, Hayes, David, Metodi, Tzvetan S., Potter, Andrew C.
Institutions: Quantinuum (United States), Quantinuum (United Kingdom)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223060522