Issue 1 | arXiv quant-ph, 16 October 2026

A trapped-ion processor runs error correction well below threshold

Our understanding

Slide 1: Bigger error protection, twelve times fewer errors. Measured on Quantinuum’s Helios: each step up in size cut errors about twelvefold, a wide margin below the threshold. 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, 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. Errors fell about twelvefold per step up in size, best result about 5 errors in a million rounds. Three triangles of growing size for 7, 19 and 37 qubits, divided by 12 between each. Link to anyon.news.
Slide 1 of 6

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.

The details

Figure 1 of the paper: (a) triangular colour codes at distances 3, 5 and 7, gold dots are physical qubits; (b) the circuit that measures the stabilisers; (c) the logical error rate per round falls from about 5 × 10⁻⁴ at distance 3 to about 5 × 10⁻⁶ at distance 7, a suppression factor Λ of about 12.
Figure 1 of Lavasani et al., arXiv:2610.24077, CC BY 4.0. Unmodified.

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 trapped-ion processor. With measures against leakage in both circuits and hardware, they reached logical error rates as low as 5 (+4/−2) × 10⁻⁶, and 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 with a suppression factor Λ = 9 (+8/−3). They compared standard decoders with neural-network decoders that decode in real time, an order of magnitude faster than the syndromes arrive.

Why it matters

A suppression factor of about 12 per distance step is a large margin below threshold, and 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 abstract 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.

What is still open

How do rate, suppression factor and decoder speed hold up when many logical qubits run in parallel and the machine grows? (our inference; the abstract does not state qubit counts beyond the code distances)

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