BeliefMatching

An implementation of the belief-matching decoder, using pymatching for the minimum-weight perfect matching (MWPM) subroutine and the ldpc library for the belief propagation (BP) subroutine. Belief-matching is more accurate than the MWPM decoder alone when hyperedge error mechanisms are present in the error model. Belief-matching has the same worst-case complexity as minimum-weight perfect matching, and the expected running time is roughly linear in the size of the decoding problem (Tanner graph). See the paper for more details.

However, note that this implementation is much (>100x) slower than just using the pymatching (v2) decoder alone, since it has not been optimised for performance. For example, for each shot, belief propagation is run on the full Tanner graph (stim DetectorErrorModel) with the output used to construct a new instance of a pymatching Matching object. This implementation uses the ldpc library for BP, which uses a parallel BP schedule, and does not support the serial BP schedule shown to have slightly improved accuracy for belief-matching in the appendix of this paper.

Installation

To install beliefmatching, run:

pip install beliefmatching

To install from source, run:

pip install -e .

from the root directory.

Usage

Here is an example of how the decoder can be used directly with Stim:

import stim
import numpy as np
from beliefmatching import BeliefMatching

num_shots = 100
d = 5
p = 0.007
circuit = stim.Circuit.generated(
    "surface_code:rotated_memory_x",
    rounds=d,
    distance=d,
    before_round_data_depolarization=p,
    before_measure_flip_probability=p,
    after_reset_flip_probability=p,
    after_clifford_depolarization=p
)

sampler = circuit.compile_detector_sampler()
shots, observables = sampler.sample(num_shots, separate_observables=True)

bm = BeliefMatching(circuit, max_bp_iters=20)

predicted_observables = bm.decode_batch(shots)
num_mistakes = np.sum(np.any(predicted_observables != observables, axis=1))

print(f"{num_mistakes}/{num_shots}")  # prints 4/100

Note that, as well as loading directly from a stim.Circuit as above, you can also load from a stim.DetectorErrorModel. When using this option it is important that decompose_errors=True is set when calling circuit.detector_error_model. E.g.:

dem = circuit.detector_error_model(decompose_errors=True)
bm = BeliefMatching(dem, max_bp_iters=20)

Sinter integration

To integrate with sinter, you can use the beliefmatching.BeliefMatchingSinterDecoder class, which inherits from sinter.Decoder. To use it, you can use the custom_decoders argument when using sinter.collect:

import sinter
from beliefmatching import BeliefMatchingSinterDecoder

samples = sinter.collect(
    num_workers=4,
    max_shots=1_000_000,
    max_errors=1000,
    tasks=generate_example_tasks(),
    decoders=['beliefmatching'],
    custom_decoders={'beliefmatching': BeliefMatchingSinterDecoder()}
)

A complete example using sinter to compare beliefmatching with pymatching can be found in the examples/surface_code_threshold.py file (this file also includes a definition of generate_example_tasks() used above).

Tests

Tests can be run by installing pytest with

pip install pytest

and running

pytest tests

Attribution

When using beliefmatching for research, please cite the paper:

@article{PhysRevX.13.031007,
  title = {Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes},
  author = {Higgott, Oscar and Bohdanowicz, Thomas C. and Kubica, Aleksander and Flammia, Steven T. and Campbell, Earl T.},
  journal = {Phys. Rev. X},
  volume = {13},
  issue = {3},
  pages = {031007},
  numpages = {20},
  year = {2023},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.13.031007},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.13.031007}
}