diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..1a21d9fda307376c5d1ae0707a597b57386ef797 --- /dev/null +++ b/README.md @@ -0,0 +1,138 @@ +--- +license: mit +library_name: pytorch +tags: + - quantum-computing + - quantum-error-correction + - surface-code + - syndrome-decoding + - physics +datasets: + - Bauxitiego/surface-code-syndromes +--- + +# Neural decoders for the surface code + +Weights from a study of when learned decoders beat minimum-weight perfect matching, and why. +Anyone can train a network to decode a surface code; that has been done since 2017. The +question here is narrower. Matching is near-optimal when its noise model is right, so the +only place a learned decoder can win is where that model is wrong. This measures how much it +wins by, and at what point it stops. + +Three architectures, all within 1.2x of each other on parameter count and given identical +optimiser, schedule and step budget. Comparing a big model to a small one, or one tuned +harder than another, measures capacity or patience rather than architecture. + +## Using a checkpoint + +Weights, the decision threshold picked on validation, and the padding mask all travel in the +same file. A checkpoint that makes you reconstruct the threshold by hand is not really +reusable. + +```python +import torch +ckpt = torch.load("mlp_A_d3_r3_p0.003.pt", weights_only=False) +print(ckpt["architecture"], ckpt["distance"], ckpt["p"], ckpt["logical_error_rate"]) +``` + +Model definitions live in [github.com/Bauxitiego/qec-neural-decoder](https://github.com/Bauxitiego/qec-neural-decoder). +Filenames encode architecture, regime, distance, rounds and physical error rate. + +## The result + +Regime B holds total noise constant and varies only its structure: the base error rate is +scaled down by bisection until detection-event density matches the uniform control, so a +"correlated noise" arm cannot secretly be a "more noise" arm. Matching is run twice, once +with the true noise model and once with the uniform one it would actually have on hardware. + +| d | noise | MWPM true | MWPM mis-spec | penalty | best neural | vs mis-spec | +|---|---|---|---|---|---|---| +| 3 | `s0_x0` | 0.00652 | 0.00652 | 1.00x | 0.00617 | indistinguishable | +| 3 | `s0_x0.0005` | 0.01531 | 0.02835 | 1.85x | 0.01536 | neural | +| 3 | `s1.75_x0` | 0.00639 | 0.00656 | 1.03x | 0.00591 | neural | +| 3 | `s1.75_x0.0015` | 0.01974 | 0.03949 | 2.00x | 0.02006 | neural | +| 3 | `s1_x0` | 0.00695 | 0.00702 | 1.01x | 0.00646 | neural | +| 3 | `s1_x0.0005` | 0.01229 | 0.02002 | 1.63x | 0.01195 | neural | +| 5 | `s0_x0` | 0.00334 | 0.00334 | 1.00x | 0.01111 | mwpm | +| 5 | `s0_x0.0005` | 0.01603 | 0.02194 | 1.37x | 0.03611 | mwpm | +| 5 | `s1.75_x0` | 0.00290 | 0.00335 | 1.16x | 0.01052 | mwpm | +| 5 | `s1.75_x0.0015` | 0.02515 | 0.03575 | 1.42x | 0.04158 | mwpm | +| 5 | `s1_x0` | 0.00317 | 0.00356 | 1.12x | 0.01507 | mwpm | +| 5 | `s1_x0.0005` | 0.01117 | 0.01439 | 1.29x | 0.02854 | mwpm | + +At distance 3 the networks track true-model matching and beat the mis-specified version by up +to 2.00x. Two rows are worth reading closely. Per-qubit rate spread on its own barely +costs matching anything, around 1.01x, because a mis-weighted graph is still roughly the +right graph. Crosstalk costs it 1.85x, because correlated errors have no edge to live on. +Rate variation is survivable; correlation is not. + +At distance 5 matching wins every row. The next section is why. + +## Why distance 5 loses + +| training shots | epochs | logical error rate | vs MWPM | +|---|---|---|---| +| 120,000 | 8 | 0.04079 | 12.1x | +| 400,000 | 25 | 0.01814 | 5.4x | +| 800,000 | 40 | 0.01118 | 3.3x | + +The sweep above ran at 400,000 shots and 12 epochs, between the first two rows. At distance 3 the networks saturate by the second row and settle slightly under matching. At distance 5 they are still improving at the largest budget tested, going 12.1x to 5.4x to 3.3x without flattening. + +So the distance-5 numbers are a statement about how long I trained. Read them as an architecture result and you will draw the wrong conclusion, which is the whole reason this section is here. + +## Regime A: uniform noise + +The control. Matching's model is exactly right here, so it should win, and mostly it does. + +| d | p | trivial | MWPM | best neural | arch | winner | +|---|---|---|---|---|---|---| +| 3 | 0.001 | 0.02308 | 0.00072 | 0.00092 | mlp | indistinguishable | +| 3 | 0.003 | 0.06567 | 0.00641 | 0.00617 | mlp | indistinguishable | +| 3 | 0.005 | 0.10454 | 0.01668 | 0.01609 | mlp | indistinguishable | +| 3 | 0.01 | 0.18744 | 0.06056 | 0.05562 | mlp | neural | +| 5 | 0.001 | 0.05801 | 0.00010 | 0.00262 | gnn | mwpm | +| 5 | 0.003 | 0.15393 | 0.00338 | 0.01111 | gnn | mwpm | +| 5 | 0.005 | 0.22917 | 0.01401 | 0.03736 | gnn | mwpm | +| 5 | 0.01 | 0.35625 | 0.08121 | 0.15477 | gnn | mwpm | + +One row is not a tie: at distance 3 and p=0.01 the MLP beats matching outright with +non-overlapping intervals. That was not the expected outcome in the regime designed to +favour matching. + +The architecture ordering also flips with distance. The plain MLP is best at distance 3, the +graph network at distance 5. The graph prior costs more than it returns until the code is +large enough for the structure to carry information. + +## Real device: Google Sycamore + +Syndromes from Google's 2023 experiment, with their own published decoder predictions as +baselines, scored on identical held-out shots. No reimplementation sits between these models +and the comparison. + +| d | rounds | trivial | pymatching | correlated | best neural | vs pymatching | +|---|---|---|---|---|---|---| +| 3 | 5 | 0.29340 | 0.14790 | 0.13760 | 0.15720 | indistinguishable | +| 3 | 25 | 0.49010 | 0.43020 | 0.42410 | 0.48920 | mwpm | +| 5 | 5 | 0.38690 | 0.14730 | 0.12750 | 0.26430 | mwpm | + +These lose, and the 25-round row loses badly enough to be worth stating plainly: 0.489 +against a trivial floor of 0.490 means the model learned essentially nothing. Each experiment +has 50,000 shots, so 35,000 to train on, against a 200-detector input with a base flip rate +near 50 percent. That is not enough supervision, and no amount of architecture fixes it. + +It is also the most practically useful thing in this repo. Simulated syndromes are free. +Hardware shots are not, and the shot budget is what actually limits learned decoders on real +machines. + +## Scope + +Distance 3 and 5, one code, one crosstalk model. The architectures are standard; the +measurement is the part that is mine. State of the art is AlphaQubit from Google DeepMind, +which used far more compute and real device data, and nothing here competes with it. +Regimes A and B are simulated, so leakage and calibration drift are absent. The distance-5 +models remain budget-limited. + +## License + +MIT for code and weights. The device evaluation uses data released by Google Quantum AI under +CC-BY-4.0; attribution is on the dataset card. diff --git a/RESULTS.json b/RESULTS.json new file mode 100644 index 0000000000000000000000000000000000000000..749632d44fb28b838b612cd3a12ada0ebe4d610e --- /dev/null +++ b/RESULTS.json @@ -0,0 +1,353 @@ +{ + "regime_a": [ + { + "d": 3, + "p": 0.001, + "trivial": 0.02308, + "mwpm": 0.00072, + "mlp": 0.000916, + "convgru": 0.001246, + "gnn": 0.001298, + "best_neural": "mlp", + "verdict": "indistinguishable", + "ratio_mwpm_over_neural": 0.7860262008733625 + }, + { + "d": 3, + "p": 0.003, + "trivial": 0.065665, + "mwpm": 0.00641, + "mlp": 0.006174, + "convgru": 0.006862, + "gnn": 0.008296, + "best_neural": "mlp", + "verdict": "indistinguishable", + "ratio_mwpm_over_neural": 1.0382248137350178 + }, + { + "d": 3, + "p": 0.005, + "trivial": 0.104545, + "mwpm": 0.016680407391677286, + "mlp": 0.016088, + "convgru": 0.017218, + "gnn": 0.01842, + "best_neural": "mlp", + "verdict": 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