VKVivek Kumar

SURFACE-CODE DECODING / INTERACTIVE RESEARCH LAB

Make an error. Test a decoder.

Change the errors on nine data qubits. A trained neural network and a conventional matching decoder estimate the logical error from the syndrome alone.

01 / Inject Pauli errors

Distance 3 · perfect measurements. Click each qubit to cycle I (none), X (bit flip), Y (both), Z (phase flip).

Loading the verified model…

All inference runs in your browser. The simulator uses known errors to score the outcome; the neural network sees only the eight syndrome bits.

02 / Decode the syndrome

Z checks · reveal X components

X checks · reveal Z components

Neural recovery on data qubits

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Recovery always clears the syndrome. A logical error can still remain: a quiet syndrome alone does not prove success. This demo uses the distance-3 model with seed 101 and its fixed matching reference.

HELD-OUT EXPERIMENTS / THREE TRAINING SEEDS

Where does machine learning help?

Noise pMWPM errorRevised ML errorRelative reductionAdjusted significance

300,000 held-out trials per row. Positive reduction favors ML. Significance uses paired exact tests with Holm correction over all 16 comparisons. The fresh demo trials above are separate from these fixed benchmark results.

IMPLEMENTATION

From syndrome to logical recovery

  1. Simulate the physical noise and measure parity checks.
  2. Apply a fixed preliminary recovery that matches the syndrome.
  3. Use a 256/64 neural network to predict the remaining logical class.
  4. Evaluate against MWPM on the same held-out trials.

The follow-up trained 12 models on 12.58 million samples and evaluated 4.8 million held-out trials. Training, validation and test sampling streams are separate.

All 256 possible distance-3 syndromes were checked for browser/Python prediction agreement. Exhaustive enumeration of all 4⁹ Pauli error patterns independently verifies the distance-3 decoding result.

Source and trained modelsBenchmark CSV

WHAT THE EVIDENCE SUPPORTS

Useful gains. Clear boundaries.

With perfect measurements at p = 0.1, revised ML reduced logical errors by 10.7% at distance 3 and 4.6% at distance 5 versus separate-X/Z MWPM. The neural decoder can use correlations that this conventional baseline treats separately.

With noisy gates, resets and measurements, MWPM still performs better. A general speed advantage, hardware readiness and a novel research contribution have not been established.

The two noise settings use different failure definitions and different meanings of p. Their absolute error rates should not be compared directly.

Method adapted from Overwater, Babaie & Sebastiano (2022). This is a smaller CPU study, not a reproduction of their FPGA/ASIC implementation.

Paired comparisonsExact distance-3 analysis