Quantinuum reported lower logical memory error rates on its Helios-1 processor as it increased the distance of a triangular color code from 3 to 7. The results, announced on October 19, 2026, cover memory and two-qubit gate benchmarks; the paper identifies below-threshold color-code magic-state preparation as a remaining step toward a full universal fault-tolerant computation.
What the Helios-1 experiment measured
Quantum error correction encodes information across physical qubits and uses measurements called syndromes to detect errors affecting the encoded, or logical, information. Quantinuum’s research team tested triangular color codes at distances 3, 5 and 7 on its trapped-ion processor Helios-1. A memory block used 13 physical qubits at distance 3, 37 at distance 5 and 73 at distance 7.
The memory test measured the probability of a logical error per syndrome-extraction cycle. That is a different quantity from the error rate in a gate benchmark, so the two results need separate units.
Memory error rates and sample sizes
Using the Tesseract decoder, Quantinuum reported lower memory error rates at each tested increase in code distance. The table lists the paper’s reported 1σ (68%) Wilson intervals alongside the number of shots, rounds and failures at each distance.
| Code distance | Physical qubits per memory block | Error per syndrome-extraction cycle | 1σ Wilson interval | Shots | Rounds per shot | Failures |
| 3 | 13 | 5.5 × 10⁻⁴ | +0.4/−0.4 × 10⁻⁴ | 15,840 | 20 | 178 |
| 5 | 37 | 3.8 × 10⁻⁵ | +1.0/−0.8 × 10⁻⁵ | 21,600 | 20 | 17 |
| 7 | 73 | 5 × 10⁻⁶ | +4/−2 × 10⁻⁶ | 29,000 | 20 | 3 |
A shot is one trial containing 20 syndrome rounds. At distance 7, the 29,000 shots amount to 580,000 shot-rounds, with three failures. The rounds are part of those trials, not additional independent shots. The paper estimates the rates from the measurement at 20 rounds because rare failures make estimates across several round counts difficult.
The fitted memory-suppression factor also depends on the decoder. It describes the paper’s estimate of how the error rate changes with each increase in code distance.
| Decoder | Fitted memory-suppression factor |
| Tesseract | 12 (+3/−2) |
| Frontier | 11 (+2/−2) |
| CNN | 7 (+1/−1) |
| RTT | 8 (+1/−1) |
The factor of 12 is the Tesseract fit, not a shared estimate across all four decoders.
The separate two-qubit benchmark
Quantinuum also reported randomized benchmarking of logical two-qubit Clifford operations. Its error rate is measured per logical two-qubit Clifford, rather than per memory cycle.
| Benchmark condition | Error probability per logical two-qubit Clifford |
| Unencoded | 9.5 × 10⁻⁴ (+0.6/−1.4 × 10⁻⁴) |
| Code distance 3 | 7 × 10⁻⁴ (+1/−1 × 10⁻⁴) |
| Code distance 5 | 7 × 10⁻⁵ (+3/−3 × 10⁻⁵) |
The experiment did not run this two-block benchmark at distance 7 because Helios-1 did not have enough qubits for two distance-7 blocks. The gate results therefore cover unencoded operations and encoded blocks at distances 3 and 5.
Leakage, decoding and the remaining milestone
Three hardware-level repump cycles suppressed the measured leaked population by a factor of 6.5(1). Compared with circuit-level leakage reduction alone, the paper reports logical-error-rate improvements of 4× at distance 3 and 8× at distance 5.
The decoding in the experiment was offline. To measure processing time, the researchers fed stored syndrome data to streaming decoders one round at a time. The paper reports average processing times below one millisecond per round on an NVIDIA H100 GPU. Its CNN and round-token transformer decoders were trained on emulator data and applied to hardware data without fine-tuning. These timing measurements were not live, end-to-end feedback during the quantum experiment.
The paper identifies below-threshold scaling of high-fidelity color-code magic-state preparation as work still needed before a full encoded Clifford-plus-T circuit demonstration. The Helios-1 results report progress on memory and two-qubit Clifford benchmarks; they do not report that full universal fault-tolerant computation.
