Issue 1 | arXiv quant-ph, 16 October 2026

A trapped-ion processor runs error correction well below threshold

Preprint, not yet peer-reviewed | Experiment

It shows colour-code error correction on a commercial trapped-ion processor with errors falling about twelvefold per step in code size, measured on hardware.

Corrected on 23 October 2026

Our understanding

Slide 1: Bigger error protection, twelve times fewer errors. Measured on Quantinuum’s Helios, preprint. Each step up in size cut errors about twelvefold, decoded afterwards on a computer. A triangle of seven qubits with one flipped qubit and the two tiles touching it raising flags.Slide 2: Every qubit is fragile. A row of seven qubits, one flipped by a disturbance.Slide 3: So one qubit is spread over seven. Coloured tiles check the qubits at their corners. The two tiles touching the flipped qubit raise a flag.Slide 4: Bigger patch, fewer errors. Errors per round, measured on Helios, decoded offline. Distance 7: 5 (+4/−2) in a million. Values read from Figure 1c and rounded: about 5 in 10,000 with 7 qubits, about 4 in 100,000 with 19 and about 5 in a million with 37, labelled about ÷12 per step.Slide 5: But only if every qubit is good enough. Schematic: adding qubits leads to more errors above a threshold (too noisy) and to fewer errors below it (good enough).Slide 6: Helios is well below the threshold. About twelvefold fewer errors with each step up in size, with the best offline decoder. The three measured colour codes drawn as triangles of 7, 19 and 37 qubits with their check tiles, errors per round read from Figure 1c and rounded: about 5 in 10,000, 4 in 100,000 and 5 in a million. Link to quanticious.com.
Slide 1 of 6

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Quantum computers make mistakes. The fix is to spread each piece of information over many qubits, so that errors can be found and corrected. This only pays off if the hardware is already good enough, and on Quantinuum’s Helios machine it is. Each time the protection was made bigger, the remaining errors dropped about twelvefold. The best result was about 5 errors in a million rounds, with an uncertainty range of 3 to 9. The errors were worked out afterwards on a computer, not yet during the run. The paper is a preprint.

The details

Figure 1 of the paper. (a) Triangular colour codes at distances 3, 5 and 7, gold dots are physical qubits, with six distance-3 and two distance-5 codes run side by side. (b) The circuit that measures the stabilisers. (c) Logical error rate per round on Helios-1 and in simulation, both decoded with Tesseract, falling from about 5 × 10⁻⁴ at distance 3 to about 5 × 10⁻⁶ at distance 7, with Λ = 12 (+3/−2).
Figure 1 of Lavasani et al., arXiv:2610.24077, CC BY 4.0. Unmodified.

Key number: Logical error 5 (+4/−2) × 10⁻⁶ per round at distance 7 and Λ = 12 (+3/−2) per distance step, memory experiment decoded offline with Tesseract

What they did

Quantum error correction only pays off once the hardware’s error rate is below a critical threshold. From then on, making the code bigger (a larger “distance”) suppresses logical errors exponentially. The team ran triangular colour codes at distances 3, 5 and 7 on Quantinuum’s Helios-1 trapped-ion processor, as memory experiments with 20 rounds of error correction. With measures against leakage in both circuits and hardware, they reached logical error rates as low as 5 (+4/−2) × 10⁻⁶ per round at distance 7. With the near-optimal Tesseract decoder, each step up in distance cut the logical error by a factor Λ = 12 (+3/−2). Encoded two-qubit Clifford operations at distance 5 reached a logical error of 7 (±3) × 10⁻⁵ per gate, with Λ = 9 (+8/−4) between distances 3 and 5. The team also tested neural-network decoders whose processing time per round is short enough in principle for real-time use. With these decoders Λ was 7 to 8. All decoding in the paper was done offline.

Why it matters

A suppression factor of about 12 per distance step is a large margin below threshold. The authors write that these rates approach what “megaquop-scale” computation needs, machines that run on the order of a million operations without a logical fault (our inference: the paper uses the term without defining it). They also argue that scaled trapped-ion processors could reach useful performance with substantially smaller code blocks than previous results on other qubit types suggested. The paper is a preprint and not yet peer-reviewed.

What is still open

The paper names what is still missing for a full computer: below-threshold preparation of magic states in the colour code. Decoding on the machine during the run is also not yet shown, since all decoding so far was done offline.

The authors note: “while all decoding in this work has been done offline” (Decoding, main text)

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