The decoder’s detector error model¶

Every task carries the detector error model (DEM) its decoder uses: sampler.task.detector_error_model from compile_sampler, or as_sinter_task(...).detector_error_model. It describes the noise Maestro simulates, overrides included, so the decoder always knows the strength of the noise it is decoding.

The Pauli twirl of what is simulated¶

The DEM is built from twirled_circuit: the circuit Maestro runs plus the Pauli twirl of every maestro.NoiseModel layer, placed after each gate as Maestro injects it:

Layer	Its twirl in the DEM
`p_1q`, `p_2q` depolarizing	the same `DEPOLARIZE1`, `DEPOLARIZE2` (exact)
coherent over-rotation	`DEPOLARIZE1(coherent)` (exact)
`T1` decay γ, on `DensityMatrix` and `MatrixProductOperator` (amplitude damping)	`PAULI_CHANNEL_1(γ/4, γ/4, (1-√(1-γ))²/4)`
`T1` decay γ, on every other type, the automatic choices included (reset to \|0⟩)	`PAULI_CHANNEL_1(γ/4, γ/4, γ/4)`, which dephases about twice as fast
`readout_error`	composed with each measurement’s own flip

For 'pauli' without overrides the DEM is the input circuit’s own. For 'none', which simulates no noise, the decoder keeps the input circuit’s DEM as its prior.

The twirl as a baseline¶

twirled_circuit returns that circuit. Sampling it, with the default 'pauli', which runs a circuit’s own noise as it is, gives the Pauli-twirled baseline:

coherent = backend.compile_sampler(noisy, noise_type='coherent', seed=1)
twirl = backend.compile_sampler(backend.twirled_circuit(noisy, noise_type='coherent'), seed=1)

Both are decoded with the same DEM, so the gap between a 'coherent' run and a run of its twirled circuit is the effect of coherence alone. See Coherent noise.

Decoding with your own decoder¶

Build the decoder from the task’s DEM:

import pymatching

sampler = backend.compile_sampler(noisy)
matcher = pymatching.Matching.from_detector_error_model(sampler.task.detector_error_model)

Don’t build it from another Stim conversion of the same Deltakit circuit. Deltakit’s PyMatchingDecoder.construct_decoder_and_stim_circuit orders gates and detectors differently from as_stim_circuit(), so its decoder doesn’t match the detection events Maestro returns.

Codes whose errors aren’t graphlike¶

The DEM is decomposed into graphlike errors for matching decoders where it can be. qLDPC codes such as Deltakit’s BivariateBicycleCode have errors that can’t be, so their DEM is left whole. Decode those with a decoder such as BP-OSD, as example_deltakit_codes.py does with ldpc on the [[72,12,6]] bivariate bicycle code.