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QEC Invariant Compendium: Baseline Equivalence, Trace-Indexed Reuse, Decoder Pipelines, and Dark-State Observables

Trent Slade

Published Oct 15, 2026• 0 citations
Publisher

Abstract

This compendium presents four revised studies of deterministic computation, reusable intermediate results, and transformation invariants in belief-propagation diagnostics and quantum error-correction software. It connects earlier QSOL-IMC preprints with commit-pinned QEC source snapshots, reproducible experiments, and machine-checked mathematical models. The four studies examine baseline equivalence between min-sum decoding and unit-weight uniformly reweighted belief propagation; trace-indexed reuse of sign vectors and CRC32 values; the interaction of clipping, damping, freezing, and ternary projection in decoder transformation pipelines; and the interpretation of local “dark-state” observables in belief-propagation traces. The deposit contains four revised papers, editable manuscript sources, a dependency-free Lean 4 project, source snapshots, validation scripts, measured results, proof logs, provenance records, and integrity manifests. The formalization comprises 43 compiled theorem declarations. Empirical validation includes 576 paired decoder cases, 80 cached-versus-inline diagnostic comparisons, a reproduced reduction from 81 to 20 sign computations, 204 selected historical tests, and 18 synthetic dark-state scenario runs. The analysis also documents counterexamples and boundary conditions involving CRC32 collisions, cache provenance, source mutation, damping, NaN handling, transformation order, and the distinction between observed local stability and safe computational reuse. The Lean proofs establish properties of the stated exact mathematical models. They do not constitute a complete refinement proof for the Python/NumPy implementations or IEEE-754 arithmetic, nor do they establish physical quantum-hardware correctness or justify skipping live-decoder updates. Historical runtime improvements are identified as previously reported results, separate from the measurements reproduced in this deposit.

DOI
10.5281/zenodo.23385691

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QECTOR-Decoder-v3 is a high-throughput, multi-backend quantum error correction (QEC) decoding suite implemented in compiled native Rust with native Python bindings via PyO3. Designed for high-performance computing (HPC) environments, low-latency quantum hardware pipelines, and offline zero-egress research, the engine bridges theoretical stabilizer formalisms with hardware-level decoding execution. This archival release includes the formal technical specification, architectural reference manual, cryptographic proof suite, and reproducible Linux/x86_64 verification harness for version 1.0.0. Key Architectural Components Native Compiled Core: High-performance Rust backend exposing zero-copy FFI bindings to Python (CPython 3.9–3.13) via PyO3. Multi-Backend Decoding Library: Includes implementations of Blossom Minimum Weight Perfect Matching (MWPM), FastUnionFind, Belief Propagation with Ordered Statistics Decoding (BP-OSD), Belief-Matching, and an AutoDecoder multi-tier fallback architecture. Hardware Interoperability: Drop-in compatibility with standard QEC formats and frameworks (Stim, PyMatching, Sinter) with Rayon multi-threading and CUDA/OpenCL acceleration hooks. Model Context Protocol (MCP) Integration: Native stdio JSON-RPC tool surfaces supporting automated syndrome decoding, check-matrix validation, and real-time telemetry profiling. Included Proof Artifacts & Verification Bundle This release contains the complete, cryptographic proof suite validating numerical correctness, memory layout, and statistical bounds: certified_proof.json & certified_proof.json.sha256: Tamper-evident execution logs confirming 100% syndrome faithfulness ($H \cdot c = s$) across all evaluation checkpoints. wilson_interval.png / .svg: Exact 95% Wilson score confidence interval statistical sweeps across code distance ranges ($d=3$ through $d=7$). syndrome_faithfulness.png / .svg: High-resolution visual parity validation and check-matrix verification charts. workspace_strides.png / .svg: Cache-line memory alignment and SIMD stride profiling diagnostics. certified_report.pdf & certified_report.md: Formal verification report and reproduction methodology. verify_artifacts.py & test_qector_decoder_v3_proofs_linux.py: Automated Python/Linux validation scripts to independently recompute and verify SHA-256 signatures and artifact integrity. Reproduction & Verification To verify the included artifact bundle locally: Bash python3 verify_artifacts.py python3 test_qector_decoder_v3_proofs_linux.py Licensing & Metadata License: PolyForm Noncommercial / Proprietary Commercial (iD01t Productions) PyPI Distribution: qector-decoder-v3 Keywords: Quantum Error Correction, Surface Codes, Rust, PyO3, Stabilizer Decoders, MWPM, BP-OSD, Union-Find, Fault-Tolerant Quantum Computing, Model Context Protocol (MCP). License terms. The software, scripts, and code in this record (including the Python verification scripts and the inlined pure-Python ground truth) are licensed under the PolyForm Noncommercial License 1.0.0: noncommercial use only. Any commercial use requires a separate commercial license from iD01t Productions. Documentation, reports, and figures in this record are made available under the Creative Commons Attribution 4.0 International License (CC-BY-4.0) with credit to Guillaume Lessard / iD01t Productions. Copyright (c) 2026 Guillaume Lessard / iD01t Productions. All rights reserved except as expressly granted above.

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QECTOR Decoder v3 (v0.6.6) - User Manual

Guillaume Lessard

QECTOR Decoder v3: The Official User Manual The authoritative, hands-on guide to high-performance quantum error-correction (QEC) decoding. As quantum computing architectures scale toward practical utility, mitigating physical noise remains the single greatest hurdle to achieving fault tolerance. Sitting directly on the critical path of every fault-tolerant quantum computer is the decoder—the vital classical algorithm responsible for rapidly translating noisy, measured error syndromes into valid physical corrections. QECTOR Decoder v3: The Official User Manual is the definitive engineering guide, backed by real performance artifacts, to utilizing the QECTOR software ecosystem for rapid quantum error-correction development, evaluation, and hardware acceleration. Fully aligned with the official v0.6.6 documentation package, this manual demystifies how QECTOR pairs a high-performance compiled Rust core with a developer-friendly Python API to deliver compiled-language speed without sacrificing scripting ergonomics. Whether you are looking to benchmark standard distance repetition codes or deploy cutting-edge quantum Low-Density Parity-Check (qLDPC) and bivariate bicycle decoders, this manual outlines everything you need to hit the ground running. Key Technical Features Covered: Comprehensive Decoder Library: Deep-dives into fast approximate decoders (Union-Find and SIMD-friendly FastUnionFind), exact minimum-weight perfect matching (Blossom MWPM), and near-optimal SparseBlossom. Belief Propagation & qLDPC Frameworks: Master advanced research and accuracy modes, including BP-OSD (BpOsdDecoder), batched GPU-resident belief propagation (bp_cupy), and correlated-noise BeliefMatching. Hardware-Accelerated Batching: Scale simulations to millions of shots per second using multi-threaded CPU execution (Rayon) and on-device GPU acceleration utilizing CUDA and OpenCL. Ecosystem Interoperability: Seamlessly integrate QECTOR with industry-standard QEC tools via built-in compatibility layers for Stim Detector Error Models (DEMs), PyMatching drop-in replacements, and Sinter Monte Carlo benchmarking sweeps. Automated Routing & Scale-Out: Let QECTOR’s intelligent AutoRouter dynamically select and cache the ideal decoder based on your hardware, batch size, and target code family. Streaming & Multi-Round Orchestration: Implement sliding-window decoders and streaming sessions to handle continuously active, multi-round phenomenological decoding. Inside the v0.6.6 Release: This manual includes the fully reproduced, peer-verified QECTOR Workbench Master Report (v0.6.6). It features zero mocked data. Every performance metric—spanning tail latencies (P99), cold-start times, memory footprints, and logical error rate (LER) threshold sweeps—is rigorously measured, archived under Zenodo DOI: 10.5281/zenodo.21320543, and 100% reproducible on your local machine. Perfect for the quantum software engineer who wants to be productive in an afternoon, as well as the academic researcher parsing high-throughput syndromes, this book is your blueprint for modern QEC simulation and decoding. Resources & Licensing: Project Page & PyPI Wheels: Search for qector-decoder-v3 Official Website & Licensing Portal: www.qector.store Source Repository: github.com/GuillaumeLessard/qector-decoder Commercial Licensing & Inquiries: admin@qector.store (Free for personal, academic, and non-commercial research; commercial R&D and product integration require a paid license).

•Jul 14, 2026•0 citations
This compendium presents four revised studies of deterministic computation, reusable intermediate results, and transformation invariants in belief-propagation diagnostics and quantum error-correction software. It connects earlier QSOL-IMC preprints with commit-pinned QEC source snapshots, reproducible experiments, and machine-checked mathematical models. The four studies examine baseline equivalence between min-sum decoding and unit-weight uniformly reweighted belief propagation; trace-indexed reuse of sign vectors and CRC32 values; the interaction of clipping, damping, freezing, and ternary projection in decoder transformation pipelines; and the interpretation of local “dark-state” observables in belief-propagation traces. The deposit contains four revised papers, editable manuscript sources, a dependency-free Lean 4 project, source snapshots, validation scripts, measured results, proof logs, provenance records, and integrity manifests. The formalization comprises 43 compiled theorem declarations. Empirical validation includes 576 paired decoder cases, 80 cached-versus-inline diagnostic comparisons, a reproduced reduction from 81 to 20 sign computations, 204 selected historical tests, and 18 synthetic dark-state scenario runs. The analysis also documents counterexamples and boundary conditions involving CRC32 collisions, cache provenance, source mutation, damping, NaN handling, transformation order, and the distinction between observed local stability and safe computational reuse. The Lean proofs establish properties of the stated exact mathematical models. They do not constitute a complete refinement proof for the Python/NumPy implementations or IEEE-754 arithmetic, nor do they establish physical quantum-hardware correctness or justify skipping live-decoder updates. Historical runtime improvements are identified as previously reported results, separate from the measurements reproduced in this deposit.
This document presents a formally validated optimization within the QSOL-IMC Quantum Error Correction (QEC) framework (v68.5.0). The optimization exploits a data-level invariant in belief propagation (BP) dynamics diagnostics: sign vectors and their derived CRC32 signatures are pure, deterministic functions indexed solely by trace position. This invariant enables elimination of redundant computation across multiple diagnostic metrics through trace-level precomputation and reuse. The invariant is proven via slice-level equivalence, byte-level identity, and purity arguments, and validated with deterministic instrumentation. The full test suite remains unchanged and passes completely. The optimization reduces redundant sign computations by 75.3% within BP dynamics analysis while preserving bitwise identity, convergence behavior, and reproducibility guarantees. Scope. This document covers invariant validation and diagnostic-layer optimization only. No algorithmic changes to decoding behavior are introduced.
This artifact documents a formally verified optimization in the QSOL-IMC Quantum Error Correction (QEC) framework (v68.4.1). The optimization exploits the algebraic identity that belief propagation decoding using uniformly reweighted min-sum with ρ=1.0 is bitwise identical to baseline min-sum decoding under IEEE 754 double-precision arithmetic. This invariant is proven analytically, validated across all decoder schedules, and confirmed via bitwise equality tests. The optimization removes redundant benchmark computation by reusing baseline results for the ρ=1.0 case without altering outputs, convergence behavior, or test coverage. A secondary improvement eliminates repeated reconstruction of derived data structures through deterministic precomputation. The full test suite (3779 tests) remains unchanged and passes completely. The optimization reduces preview sweep runtime by approximately 43% and overall runtime by approximately 7.6%. This artifact includes formal proof, execution-path validation, safety analysis, and reproducibility guarantees, and serves as a reference for invariant-driven optimization in deterministic QEC benchmarking systems.
This document presents a formally verified optimization within the QSOL-IMC Quantum Error Correction (QEC) framework (v68.4.1). The optimization exploits an algebraic invariant in belief propagation decoding: URW(min-sum, ρ = 1.0) ≡ baseline min-sum This equivalence is proven analytically, validated across all decoder schedules, and confirmed via bitwise identity checks under IEEE 754 double-precision arithmetic. Leveraging this invariant enables elimination of redundant computation in benchmark sweeps without altering outputs, convergence behavior, or test coverage. A secondary optimization removes repeated reconstruction of derived data structures through deterministic precomputation. The full test suite (3779 tests) remains unchanged and passes completely. The optimization yields a 43% reduction in preview sweep runtime and a ~7.6% overall runtime reduction. Scope. This document covers invariant validation and test-suite optimization only. No algorithmic changes to decoding behavior are introduced.
This work introduces a deterministic framework for identifying, validating, and falsifying structural invariants in decoder transformation pipelines. Departing from traditional performance-centric analyses of belief propagation, the study treats decoder execution as a composition of deterministic operators and focuses on invariant properties that persist under repeated application. We formally establish several classes of invariants, including ternary closure, operator idempotence, and dark-skip cascade behavior, and validate them directly against implementation through deterministic testing. In parallel, we construct explicit counterexamples to demonstrate the failure of commonly assumed properties such as universal absorbing states and global idempotence under damping. A key contribution is the introduction of invariant-guided reasoning as a mechanism for eliminating redundant computation rather than optimizing it. By reframing decoder pipelines as dynamical systems with provable algebraic structure, this work provides a foundation for deterministic runtime reduction, modular pipeline design, and future extensions into qudit-based decoding and sonification-driven analysis. This work builds on prior results in dark-state invariant detection and forms part of an ongoing research program in invariant-driven computation and quantum-inspired information dynamics.
QECTOR-Decoder-v3 is a high-throughput, multi-backend quantum error correction (QEC) decoding suite implemented in compiled native Rust with native Python bindings via PyO3. Designed for high-performance computing (HPC) environments, low-latency quantum hardware pipelines, and offline zero-egress research, the engine bridges theoretical stabilizer formalisms with hardware-level decoding execution. This archival release includes the formal technical specification, architectural reference manual, cryptographic proof suite, and reproducible Linux/x86_64 verification harness for version 1.0.0. Key Architectural Components Native Compiled Core: High-performance Rust backend exposing zero-copy FFI bindings to Python (CPython 3.9–3.13) via PyO3. Multi-Backend Decoding Library: Includes implementations of Blossom Minimum Weight Perfect Matching (MWPM), FastUnionFind, Belief Propagation with Ordered Statistics Decoding (BP-OSD), Belief-Matching, and an AutoDecoder multi-tier fallback architecture. Hardware Interoperability: Drop-in compatibility with standard QEC formats and frameworks (Stim, PyMatching, Sinter) with Rayon multi-threading and CUDA/OpenCL acceleration hooks. Model Context Protocol (MCP) Integration: Native stdio JSON-RPC tool surfaces supporting automated syndrome decoding, check-matrix validation, and real-time telemetry profiling. Included Proof Artifacts & Verification Bundle This release contains the complete, cryptographic proof suite validating numerical correctness, memory layout, and statistical bounds: certified_proof.json & certified_proof.json.sha256: Tamper-evident execution logs confirming 100% syndrome faithfulness (H⋅c=sH \cdot c = sH⋅c=s) across all evaluation checkpoints. wilson_interval.png / .svg: Exact 95% Wilson score confidence interval statistical sweeps across code distance ranges (d=3d=3d=3 through d=7d=7d=7). syndrome_faithfulness.png / .svg: High-resolution visual parity validation and check-matrix verification charts. workspace_strides.png / .svg: Cache-line memory alignment and SIMD stride profiling diagnostics. certified_report.pdf & certified_report.md: Formal verification report and reproduction methodology. verify_artifacts.py & test_qector_decoder_v3_proofs_linux.py: Automated Python/Linux validation scripts to independently recompute and verify SHA-256 signatures and artifact integrity. Reproduction & Verification To verify the included artifact bundle locally: Bash python3 verify_artifacts.py python3 test_qector_decoder_v3_proofs_linux.py Licensing & Metadata License: PolyForm Noncommercial / Proprietary Commercial (iD01t Productions) PyPI Distribution: qector-decoder-v3 Keywords: Quantum Error Correction, Surface Codes, Rust, PyO3, Stabilizer Decoders, MWPM, BP-OSD, Union-Find, Fault-Tolerant Quantum Computing, Model Context Protocol (MCP). License terms. The software, scripts, and code in this record (including the Python verification scripts and the inlined pure-Python ground truth) are licensed under the PolyForm Noncommercial License 1.0.0: noncommercial use only. Any commercial use requires a separate commercial license from iD01t Productions. Documentation, reports, and figures in this record are made available under the Creative Commons Attribution 4.0 International License (CC-BY-4.0) with credit to Guillaume Lessard / iD01t Productions. Copyright (c) 2026 Guillaume Lessard / iD01t Productions. All rights reserved except as expressly granted above.
QECTOR Decoder v3: The Official User Manual The authoritative, hands-on guide to high-performance quantum error-correction (QEC) decoding. As quantum computing architectures scale toward practical utility, mitigating physical noise remains the single greatest hurdle to achieving fault tolerance. Sitting directly on the critical path of every fault-tolerant quantum computer is the decoder—the vital classical algorithm responsible for rapidly translating noisy, measured error syndromes into valid physical corrections. QECTOR Decoder v3: The Official User Manual is the definitive engineering guide, backed by real performance artifacts, to utilizing the QECTOR software ecosystem for rapid quantum error-correction development, evaluation, and hardware acceleration. Fully aligned with the official v0.6.6 documentation package, this manual demystifies how QECTOR pairs a high-performance compiled Rust core with a developer-friendly Python API to deliver compiled-language speed without sacrificing scripting ergonomics. Whether you are looking to benchmark standard distance repetition codes or deploy cutting-edge quantum Low-Density Parity-Check (qLDPC) and bivariate bicycle decoders, this manual outlines everything you need to hit the ground running. Key Technical Features Covered: Comprehensive Decoder Library: Deep-dives into fast approximate decoders (Union-Find and SIMD-friendly FastUnionFind), exact minimum-weight perfect matching (Blossom MWPM), and near-optimal SparseBlossom. Belief Propagation & qLDPC Frameworks: Master advanced research and accuracy modes, including BP-OSD (BpOsdDecoder), batched GPU-resident belief propagation (bp_cupy), and correlated-noise BeliefMatching. Hardware-Accelerated Batching: Scale simulations to millions of shots per second using multi-threaded CPU execution (Rayon) and on-device GPU acceleration utilizing CUDA and OpenCL. Ecosystem Interoperability: Seamlessly integrate QECTOR with industry-standard QEC tools via built-in compatibility layers for Stim Detector Error Models (DEMs), PyMatching drop-in replacements, and Sinter Monte Carlo benchmarking sweeps. Automated Routing & Scale-Out: Let QECTOR’s intelligent AutoRouter dynamically select and cache the ideal decoder based on your hardware, batch size, and target code family. Streaming & Multi-Round Orchestration: Implement sliding-window decoders and streaming sessions to handle continuously active, multi-round phenomenological decoding. Inside the v0.6.6 Release: This manual includes the fully reproduced, peer-verified QECTOR Workbench Master Report (v0.6.6). It features zero mocked data. Every performance metric—spanning tail latencies (P99), cold-start times, memory footprints, and logical error rate (LER) threshold sweeps—is rigorously measured, archived under Zenodo DOI: 10.5281/zenodo.21320543, and 100% reproducible on your local machine. Perfect for the quantum software engineer who wants to be productive in an afternoon, as well as the academic researcher parsing high-throughput syndromes, this book is your blueprint for modern QEC simulation and decoding. Resources & Licensing: Project Page & PyPI Wheels: Search for qector-decoder-v3 Official Website & Licensing Portal: www.qector.store Source Repository: github.com/GuillaumeLessard/qector-decoder Commercial Licensing & Inquiries: admin@qector.store (Free for personal, academic, and non-commercial research; commercial R&D and product integration require a paid license).