Math-to-Code Traceability¶

This page maps canonical mathematical quantities to implementation loci.

Equation-to-Implementation Map¶

Mathematical Object	Representation	Primary Implementation Sources
\(s = He \bmod 2\)	syndrome parity map	src/surface/SurfaceSyndrome.cpp, src/qec/CSSSyndrome.cpp, src/utils/SyndromeUtils.cpp
\(n=2d(d-1)\), \(m_X=d^2\), \(m_Z=(d-1)^2\)	surface geometry cardinalities	examples/paper_runs/paper_04/scripts/generate_comparison_requests.py
MWPM objective \(\min \sum C_{uv}\)	defect matching cost minimization	src/surface/MWPMDecoder.cpp, src/surface/MatchingProblem.cpp, src/surface/BlossomMWPM.cpp
Union-Find cluster/peel steps	near-linear decoding heuristic	src/surface/UnionFindDecoder.cpp, src/decoders/UnionFindDecoder.cpp
BP message updates	probabilistic inference over Tanner graph	src/decoders/BeliefPropagation.cpp, src/graph/TannerGraph.cpp
\(\widehat{\mathrm{LER}}=k/N\)	trial aggregation	src/sim/MonteCarlo.cpp, src/sim/SurfaceThresholdRunner.cpp
Wilson/CI intervals	uncertainty quantification	src/surface/ScalingAnalysis.cpp, analysis scripts in examples/
TV/JS request distances	request-equivalence diagnostics	examples/paper_runs/paper_04/scripts/analyze_request_equivalence.py
Source-reference deltas	reproducible comparator metrics	examples/paper_runs/paper_04/scripts/analyze_pennylane_vs_lidmas.py
Bootstrap CIs	nonparametric uncertainty estimates	examples/paper_runs/paper_04/scripts/analyze_bootstrap_ci.py

Proof-Obligation-to-Test/Artifact Map¶

Obligation	Artifact
O1 syndrome consistency	request/replay outputs and decoder diagnostics in results/02_replay_decoder_matrix/
O2 decoder output validity	decoder_responses_*.ndjson schema and parse checks
O3 deterministic replay	fixed-seed reruns + matching stage tables
O4 comparator correctness	table_replay_matrix.csv -> table_source_vs_lidmas.csv derivation
O5 CLI/App parity	paper_04 manifest parity checks and run summaries in LiDMaS+ App

Notes¶

• This map is intentionally concrete: each math object points to one or more source files.
• As implementations evolve, update this page alongside code changes to keep trust intact.