Error correction / Comparison

QEC decoder comparison

Logical error per cycle on public Willow chip data

A decoder reads the checks a quantum chip measures every round and decides what went wrong. The fewer calls it gets wrong, the smaller the code a logical qubit needs. Every decoder here is measured on the same public surface code data from Google's Willow chips.

Badges set each Z-QEC figure against the best decoder outside ZKSF in that table: Lowest or Highest where ours leads, Level where our range or 95% interval reaches theirs, and Near level within 2%, always on the weaker end of a range. Real time gives what each source says about its decoder. Click a column to sort, and a figure's label to reach its source.

The highest Lambda on the 2024 Willow chip

Lambda is how fast a decoder's error falls as the code grows, the figure that decides how many physical qubits a logical qubit will need at scale. A white line marks our 95% interval, or our range where the figure is one.

• Z-QEC Platinum and Z-QEC Gold have the two highest Lambda values on this chip, on held-out TEST shots and on validation shots alike

Level with the Willow neural network at d7

Its published 0.143% per cycle at d7 sits inside the 95% interval of every Z-QEC figure, on held-out TEST shots and on validation shots.

The Willow paper gives its figure with one standard error, 0.003.

Fewer wrong calls than Libra, Harmony and correlated matching, on the same shots

The 2024 release includes the calls of these three decoders, so they can be scored on exactly the shots ours were. At d7, on the same 9,000 validation shots across runs of 10, 30 and 50 rounds in both bases:

• Z-QEC PlatinumZKSF362
• Z-QEC GoldZKSF384
• Libra434
• Harmony474
• Correlated matching528

• Z-QEC Platinum makes 17% fewer wrong calls than Libra, 24% fewer than Harmony and 31% fewer than correlated matching. Z-QEC Gold makes 12%, 19% and 27% fewer
• On held-out TEST shots, scored by the Willow papers' own method, Platinum makes at least 15% fewer errors per cycle than Libra at d7, and Gold 13% fewer

Every validation shot, on our own scoring

All 81,000 validation shots at d3, 36,000 at d5 and 9,000 at d7, with Libra scored the same way on the same shots.

• Platinum makes 17% fewer errors per cycle than Libra at d7 and 8% fewer at d5. Gold makes 12% and 6% fewer

Lower error than every decoder built on the public data

The 2024 Willow chip, with every published decoder that, like Z-QEC, worked from the public release or from no chip data at all.

• Z-QEC Platinum and Gold have the lowest error at every distance in this table, and the highest Lambda
• Against Riverlane's correlated matching, Platinum has at least 12% less error at d5 and 20% less at d7, and Gold 7% and 17% less

The 2026 Willow chip at d5, on the same shots

The 2026 release includes the calls of AlphaQubit 2, Tesseract and Sparse Blossom too. At d5, every decoder here is scored on the same 9,600 validation shots: 150 from each of 64 runs, across four patches, both bases and runs of 10 to 150 rounds.

Scored by us, by the Willow papers' own method, from the public 2026 release. These shots are a sample of the validation shots, so read this table on its own: its rates differ from the rates on every validation shot further down this page.

• Z-QEC Platinum and Gold make 5% fewer wrong calls than Tesseract, calibrated: 1,097 against 1,154, and 0.1637 per cycle against 0.1699
• Z-QEC Gold with no chip data has the lowest error of the decoders with no chip data: 8% less than Tesseract, SI1000 and 29% less than Sparse Blossom, SI1000
• AlphaQubit 2, trained on this chip's own data, has the lowest error here, with Platinum and Gold just behind at 4% more. What Z-QEC had to work with is set out further down

The Z basis, without the Willow neural network

One published network, from Lange et al., reports the Z basis only, trained on the chip's public shots. Here it sits beside the other decoders in the same basis.

• Platinum has 13% less error than Lange et al.'s network at d5 and 25% less at d7, and the lowest error at both
• At d3 Lange's network is 2% lower than Platinum. Lange et al. score their own split of the shots, their own way

The Z basis, with the Willow neural network

• The Willow neural network was trained on the chip's own data. With it in the table, Platinum is just behind it at every distance, and at d3 just behind Lange et al.'s network too. What Z-QEC had to work with is in the next section

Level, near level or just behind the networks trained on each chip

Each chip has a network trained on its own data: the Willow neural network in 2024 and AlphaQubit 2 in 2026. On the 2024 chip, Z-QEC Platinum has the higher Lambda, is level with the Willow neural network at d7 and just behind it at d3 and d5. On the 2026 chip, Platinum is level with AlphaQubit 2 on Lambda, near level at d3 and just behind at d5 and d7, and Gold is level on Lambda and just behind at each distance.

The 2024 Willow chip

The 2026 Willow chip, validation shots

Lowest error without any chip data

The decoders on the 2026 Willow chip that knew nothing about it beyond its circuits.

• At d3, Z-QEC Gold with no chip data has 4% less error than Tesseract and 13% less than Sparse Blossom, with the same lack of chip data, and its d5 and d7 ranges sit below both

Every figure, in full

The 2024 Willow chip

The 2026 Willow chip, validation shots

Scored by the Willow papers' own method. TEST data is available on request.