Qector Ler Methodology

QECTOR LER Methodology

Source of authority: v1.0.0 reference manual, chapters 15, 19, 22.

Definitions

• Logical error rate: the probability that the predicted observable flips differ from the sampled observable flips on the same Stim circuit. Scoring with correction != error is explicitly rejected (manual 15).
• Wilson 95% score interval: a binomial confidence interval with correct coverage at small k and extreme p, unlike the Wald approximation. Always z = 1.959963985.

Wilson formula (manual 15.2)

For k logical errors in n trials:

centre  = ( p + z^2/(2n) ) / ( 1 + z^2/n )
margin  = z * sqrt( p(1-p)/n + z^2/(4 n^2) ) / ( 1 + z^2/n )
CI_95   = ( max(0, centre - margin), min(1, centre + margin) )

with p = k/n and z = 1.959963985.

Worked example (manual 15.2, appendix E.2): k=10, n=1000 -> CI is approximately (0.00544, 0.01831). The qector-research.wilson_ci tool returns exactly this; qector-research.wilson_table returns a batch of intervals for a series of k values at fixed n.

Required-artifact metadata (manual 22.3, table 22.1)

Every evidence artifact must include:

The qector-research.artifact_metadata_check tool generates the full required-metadata block for a candidate artifact (no decoder execution). The library qector-library.threshold_sweep already emits the same block plus the chapter 22.3 SHA-256 sidecar.

Tagging rule (manual 15.3)

• Tag every LER run code_capacity or circuit_level.
• The harness refuses to compare across tags. A code_capacity LER at a nominal p is not comparable to a circuit_level LER at the same p.
• Historically some artifacts mixed a code_capacity QECTOR measurement with a circuit_level PyMatching measurement; those artifacts were withdrawn (manual 15.3 + 19.1).
• "Competitive harness drives every decoder through the same pipeline - the same Stim circuit, the same detector samples, the same DEM, the same observable scoring - so the only thing that varies between rows is the decoder."

Safe / unsafe wording (manual 22.5)

Safe (anchored to a machine, workload, and artifact):

• "on this machine, for this code/distance/noise/seed/batch configuration, decoder A had median hot-path latency X and p99 Y."
• "on this checked-in artifact, QECTOR weighted Blossom produced LER parity with PyMatching on the tested d=15 Stim workload."

Unsafe (never published):

• "decoder A is universally faster"
• "always more accurate"
• "production real-time hardware infrastructure"
• any speed superlative without a surviving artifact

Memory methodology (manual 22.4)

• Python-side: tracemalloc peak; process RSS via psutil when installed.
• Native Rust and GPU memory: backend diagnostics or vendor tools; label separately.
• Python allocation, process RSS, native heap, and VRAM are never mixed as a single metric.

Hot path vs cold path (manual 22.1)

• Cold path: decoder construction (graph build, weight preprocessing, allocation). Reported separately.
• Hot path: decode() on a pre-built decoder with syndromes already in memory. Reported as decode_hotpath_latency_us or similar.
• Reporting only the hot path is acceptable only for a clearly labelled pre-built, repeated-decode workload.

The screening-estimate caveat (manual 19, 27)

• 25 trials is a screening estimate, not a converged threshold.
• The shipped qector-researcher skill uses the word "screening estimate" whenever the trial count is small, never "converged threshold" without a dated, reproducible artifact.

How the bench server helps

• qector-research.wilson_ci and wilson_table cover the math utility without running a decode.
• qector-research.logical_coset_score scores a batch of (predicted, sampled) logical observables on the logical coset (Theorem 2) and reports a Wilson 95% interval.
• qector-research.artifact_metadata_check generates the chapter 22.3 metadata block for a candidate artifact.
• qector-research.decode_faithfulness_check re-verifies the H c = s (mod 2) gate externally (useful when ingesting corrections from a third-party decoder or older wheel build).
• qector-research.hot_path_microbench runs a per-machine hot-path latency sample. The result is never a portable claim.