Product / Error correction

Quantum error correction

Decoders measured on public chip data, and error correction for your chip

A logical qubit spreads one qubit of information across many physical qubits. Every round, the chip measures checks that flag errors without reading the information itself, and a decoder turns those flags into a correction. The better the decoder, the fewer physical qubits each logical qubit costs.

2.21

The highest Lambda on the 2024 Willow chip, Z-QEC Platinum on held-out TEST shots, against 2.14 for the Willow neural network

At least 15%

fewer errors than Libra at d7, on the same held-out shots

Level

with the Willow neural network at d7, 0.141 to 0.144% per cycle against 0.143%

Figures from offline decoding. See every decoder and its source.

Two ways to use it

For hardware makers

Z-QEC Platinum and Gold

Our own decoder for your chip. Platinum and Gold are both tuned to your chip, Platinum to our highest accuracy. Each is agreed under contract and measured on your own held-out shots, against your current decoder on the same shots

Platinum and Gold Contact us

Self-serve, in the console

Error correction

Run a surface or repetition code memory experiment up to distance 15 on standard circuit-level noise. It is decoded by minimum-weight perfect matching with PyMatching, and you get the logical error rate with a 95% interval and a ZQEC-v0.1 certificate

Open the console ZQEC-v0.1

Other chips

On IBM's Nighthawk surface code, Z-QEC Gold made 7% fewer logical errors than matching on the same shots, level with BeliefMatching. On five more chips running a repetition code, it was level with or ahead of matching on every one, and never wrong on a shot that matching decoded right.

Logical errors on other makers' chips, Z-QEC Gold and matching on the same shots, lower is better
Chip	Test	Shots	Z-QEC Gold	Matching
Nighthawk ibm_miamiSurface code, d5, 2 to 8 rounds	Surface code, d5, 2 to 8 rounds	12,288	1,946	2,090
TianyanRepetition code, d3 to d11	Repetition code, d3 to d11	102,400	38	46
BrisbaneRepetition code, d3 to d11	Repetition code, d3 to d11	102,400	27	31
WuyueRepetition code, d3 to d9	Repetition code, d3 to d9	81,920	102	105
TorinoRepetition code, d3 to d11	Repetition code, d3 to d11	102,400	9	10
SherbrookeRepetition code, d3 to d11	Repetition code, d3 to d11	51,200	6	6

Logical errors on the same shots, lower is better, with each decoder given the same published chip data. BeliefMatching made about 1,993 on Nighthawk, counted from the dataset's own figures. A brief test with small counts, on public data alone; the repetition code ran one round, on validation shots.

Data: Nighthawk ibm_miami from Drouet et al., Zenodo record 21336494; Tianyan, Wuyue and IBM's Brisbane, Torino and Sherbrooke from He Songhuan's PAEMS dataset, Zenodo record 18230210. Both under CC BY 4.0. Changes: scored by us. Names identify the data and imply no partnership or endorsement

Explore the results

Decoder Comparison

Every decoder, one set of chip data

Logical error per cycle and Lambda on the 2024 and 2026 Willow chips, each figure marked as published or scored by us

QEC Explorer

Replay real shots

Watch a chip's checks light up round by round, then see which decoders called each shot right

Platinum Z-QEC

Tuned to your chip

Z-QEC Platinum and Gold for hardware makers, measured on your own held-out shots

What is quantum error correction (QEC)?

Quantum error correction (QEC) is how a quantum computer protects its information from errors. Qubits are fragile. Heat, stray fields and imperfect control flip or blur their states far more often than the bits in an ordinary chip. QEC spreads each logical qubit across many physical qubits, so that an error on any one of them can be spotted and undone without reading the information itself.

In a surface code, the most widely studied design, the physical qubits sit on a grid. Data qubits hold the information, and the qubits between them are measured every round as checks, each reporting whether its neighbours still agree. A check whose result changes from one round to the next is a detection event, the only trace an error leaves. A decoder reads these events round after round and works out the correction. Its accuracy sets how many physical qubits each logical qubit needs, and so how large a useful quantum computer has to be.

Error correction pays off only below the threshold, when the chip's physical error rate is low enough. Then each step up in code distance, from d3 to d5 to d7, divides the logical error by a factor called Lambda, so a larger code makes fewer errors. Google's Willow chip showed this in 2024, with Lambda above 2. A better decoder raises Lambda on the same hardware, which cuts the number of physical qubits a fault-tolerant quantum computer needs.

A distance 3 surface code, with 9 data qubits in white and 8 checks, X in blue and Z in violet. A bit flip on the ringed centre qubit lights the two Z checks beside it

Quantum error correction terms

Logical qubit: One qubit of information, spread by a code across many physical qubits, the individual qubits on the chip. Algorithms run on logical qubits
Surface code: A code that lays qubits out on a square grid, data qubits and check qubits side by side. It needs links only between neighbouring qubits and copes with comparatively high error rates
Code distance: The size of a code, written d3, d5 or d7. A distance 7 surface code uses 49 data qubits and 48 check qubits, and can correct up to three errors at once
Check, or stabilizer: A measurement on a few neighbouring data qubits that shows whether an error has struck them, without disturbing the information they hold
Detection event: A check whose result changed since the round before, the trace an error leaves. The pattern of check results is called the syndrome
Decoder: Software that reads the detection events and decides which correction to apply. Minimum-weight perfect matching, union-find and neural networks are common kinds, and both speed and accuracy matter
Logical error per cycle: How often the logical qubit ends up wrong, per round of checks. Decoders are compared on it at each code distance
Lambda (Λ): The factor by which the logical error per cycle falls each time the code distance grows by two. Above 1, a larger code makes fewer errors
Threshold: The physical error rate below which adding qubits lowers the logical error rate. Above it, a larger code makes more errors
Real time decoding: Decoding fast enough to keep pace with the chip, about a microsecond per round on superconducting qubits, so each correction is ready before the next step needs it

Where every figure comes from

Each figure is either copied from the paper that published it or scored by us from the public Willow shots and public decoder outputs, and says which
Our 2024 figures are reported on validation shots and on held-out TEST shots. Our 2026 figures are on validation shots, and TEST data is available on request
How Z-QEC works is not published. Anything beyond the figures is discussed under a non-disclosure agreement