Decoding, learned.

Physical errors are the disease. Traditional correction was often worse than no treatment. Our decoder is closer to an immune system.

The wall

Quantum devices are error-prone by nature. Physical error correction is what turns fragile physical qubits into reliable logical ones — and reaching roughly 10,000 physical qubits is what unlocks the first practically useful applications, such as Shor’s algorithm.

NO DECODER

No treatment

Errors accumulate. The computation dies before it produces an answer.

RULE-BASED

Traditional medicine

Hand-engineered decoding rules work, but can’t reach the logical error rates useful computation needs.

EDENCODE

Immune system

Learned decoding: the system recognises and corrects errors, and improves as it sees more data.

Why it holds together

Four compounding advantages — not one trick.

01 · qLDPC

Efficiency of the code

Around 8 physical qubits per logical qubit, against roughly 100:1 for surface or colour codes.

02 · ERROR RATE

Where the bar is

The logical error rate must fall below 10-11. qLDPC alone does not get there with rule-based decoders — that is the bottleneck we attack.

03 · MODELS

Ultra-small by design

Below 10K parameters, so inference fits comfortably inside real-time control.

04 · HARDWARE

FPGA in the loop

Sub-microsecond latency: 0.37 µs atom rearrangement against roughly 60 µs in prior published work.

How we measure

Published figures, stated as they are.

LATENCY

0.37 µs

FPGA atom-rearrangement latency, versus ~60 µs prior art (arXiv:2210.10364) — roughly 160× faster.

OVERHEAD

~8:1

Physical-to-logical qubit ratio with qLDPC codes, versus ~100:1 for surface codes.

MODEL SIZE

<10K parameters

Small enough for real-time deployment; research decoders run into millions and billions.

TARGET

Logical error rate < 10-11

The threshold for useful, fault-tolerant computation.

Figures reflect internal benchmarks and published comparisons. Ask us for the technical details. Our Graph Transformer Decoder is open source.

Lifted-product qLDPC lattice: data qubits with X and Z check operators
The code, literally. Data qubits (blue) surrounded by X and Z check operators (orange, green) on a lifted-product qLDPC lattice — the constraint graph our decoder reads directly rather than approximating.
Decoding latency against physical error rate
Latency against physical error rate. A decoder must finish inside the qubit's coherence time. Our message-passing decoder (green) stays in the microsecond range across the whole range, where the baselines move into milliseconds. Code shown: lifted-product [[1122,148,≤20]].
Logical error rate against physical error rate
Below threshold. Logical error rate against physical error rate. Below the threshold, improving the physical qubits suppresses logical errors instead of amplifying them — the regime a fault-tolerant machine needs; the ML message-passing variants track lowest.
Atom noise maps at 20, 50, 100 and 200 milliseconds
Where the noise actually comes from. Noise maps captured at 20 / 50 / 100 / 200 ms in an atomic array — the patterns a decoder has to survive.

Benchmarks on lifted-product qLDPC codes; baselines as labelled on each figure.

Working on a quantum stack?

We work across modalities — we do not need to predict which one wins.