QECTOR MEGA 2.2.1 | Full Scientific Reference Manual and Verification Report Authors Guillaume Lessard (ORCID 0009-0000-3465-3753) / iD01t Productions Description This deposit contains the complete scientific reference manual, mathematical foundations, architecture description, API specification, and end-to-end verification record for qector-mega 2.2.1. The decoder is a high-performance residual-faithful belief-propagation with ordered-statistics decoding (BP-OSD) engine targeting the IonQ Superion 256 platform under the Walking Cat architecture (arXiv:2604.19481). It features a Rust BP-OSD core with PyO3 bindings, optional CUDA acceleration with automatic CPU fallback, and streaming dual-window support for syndrome-extraction cycle (SEC) schedules. The public decode paths enforce strict residual gating, ensuring the identity $Hc=s$ holds over $\mathbb{F}_2$ or failing explicitly. Three production codes are natively supported: Q70: $[[70, 6, 9]]$, Rank 59 Q102: $[[102, 22, 9]]$, Rank 80, exact Appendix-C construction Gross: $[[144, 12, 12]]$, Rank 112, Bivariate bicycle construction Status (15 September 2026) ALL LISTED CERTIFICATION SUITES PASS / GREEN Full Suite 205/205 | Q102 Production 59/59 | Math 38/38 | Onpager 98/98 | Compute_Certified_100 GREEN | Z3 Full SMT 31 checks GREEN | Lean 0 sorries The document consolidates original author certificates with a full re-execution of every suite on a measured Linux host (Python 3.12.3, manylinux cp312 wheel). All theorems, residual soundness arguments, performance data, Z3 oracle artifacts, and public artifacts are included. Key contents Mathematical foundations and theorems (CSS orthogonality, BP identities, residual faithfulness, and Z3 oracle soundness) Architecture and public API surface (AutoDecoder, TwoStage, SpaceTime, Hardware bridge caps) Verification results, including canonical latency, batch throughput, thread scaling, and exhaustive/noise-stress campaigns Supported codes, reproducibility instructions, licensing, and distribution limits Related deposits Frozen package (v2.2.1 Frozen Release): https://doi.org/10.5281/zenodo.22773113 LCL-832 Master Edition: https://doi.org/10.5281/zenodo.19119790 QECTOR Decoder v3: https://doi.org/10.5281/zenodo.21941046 License Public verification data and this PDF: CC-BY-4.0 Binary + source (proprietary, NDA-restricted evaluation only) Keywords quantum error correction, trapped-ion, BP-OSD, residual faithfulness, GF(2), CSS codes, formal contract testing, IonQ Superion 256, Walking Cat, Rust, PyO3 Version 2.2.1 Citation Code snippet @techreport{Lessard2026QectorMegaRefManual, author = {Lessard, Guillaume}, title = {QECTOR MEGA 2.2.1: Full Scientific Reference Manual and Verification Report}, institution = {iD01t Productions / qector.store}, year = {2026}, month = {9}, day = {15}, note = {IonQ Superion 256 / Walking Cat. Proprietary binary; public cert data CC-BY-4.0. ORCID 0009-0000-3465-3753} } Trademark and affiliation notice This is an independent product developed by Guillaume Lessard (iD01t Productions). It is not affiliated with, endorsed by, or sponsored by IonQ, Inc.; the names 'IonQ' and 'Superion' are trademarks of IonQ, Inc. and are used here solely to designate the target hardware profile.
QECTOR MEGA 2.2.1 | Full Scientific Reference Manual and Verification Report Authors Guillaume Lessard (ORCID 0009-0000-3465-3753) / iD01t Productions Description This deposit contains the complete scientific reference manual, mathematical foundations, architecture description, API specification, and end-to-end verification record for qector-mega 2.2.1. The decoder is a high-performance residual-faithful belief-propagation with ordered-statistics decoding (BP-OSD) engine targeting the IonQ Superion 256 platform under the Walking Cat architecture (arXiv:2604.19481). It features a Rust BP-OSD core with PyO3 bindings, optional CUDA acceleration with automatic CPU fallback, and streaming dual-window support for syndrome-extraction cycle (SEC) schedules. The public decode paths enforce strict residual gating, ensuring the identity Hc=s holds over F2 or failing explicitly. Three production codes are natively supported: Q70: [[70,6,9]], Rank 59 Q102: [[102,22,9]], Rank 80, exact Appendix-C construction Gross: [[144,12,12]], Rank 112, Bivariate bicycle construction Status (15 September 2026) ALL LISTED CERTIFICATION SUITES PASS / GREEN Full Suite 205/205 | Q102 Production 59/59 | Math 38/38 | Onpager 98/98 | Compute_Certified_100 GREEN | Z3 Full SMT 31 checks GREEN | Lean 0 sorries The document consolidates original author certificates with a full re-execution of every suite on a measured Linux host (Python 3.12.3, manylinux cp312 wheel). All theorems, residual soundness arguments, performance data, Z3 oracle artifacts, and public artifacts are included. Key contents Mathematical foundations and theorems (CSS orthogonality, BP identities, residual faithfulness, and Z3 oracle soundness) Architecture and public API surface (AutoDecoder, TwoStage, SpaceTime, Hardware bridge caps) Verification results, including canonical latency, batch throughput, thread scaling, and exhaustive/noise-stress campaigns Supported codes, reproducibility instructions, licensing, and distribution limits Related deposits Frozen package (v2.2.1 Frozen Release): https://doi.org/10.5281/zenodo.22773113 LCL-832 Master Edition: https://doi.org/10.5281/zenodo.19119790 QECTOR Decoder v3: https://doi.org/10.5281/zenodo.21941046 License Public verification data and this PDF: CC-BY-4.0 Binary + source (proprietary, NDA-restricted evaluation only) Keywords quantum error correction, trapped-ion, BP-OSD, residual faithfulness, GF(2), CSS codes, formal contract testing, IonQ Superion 256, Walking Cat, Rust, PyO3 Version 2.2.1 Citation Code snippet @techreport{Lessard2026QectorMegaRefManual, author = {Lessard, Guillaume}, title = {QECTOR MEGA 2.2.1: Full Scientific Reference Manual and Verification Report}, institution = {iD01t Productions / qector.store}, year = {2026}, month = {9}, day = {15}, note = {IonQ Superion 256 / Walking Cat. Proprietary binary; public cert data CC-BY-4.0. ORCID 0009-0000-3465-3753} } Trademark and affiliation notice This is an independent product developed by Guillaume Lessard (iD01t Productions). It is not affiliated with, endorsed by, or sponsored by IonQ, Inc.; the names 'IonQ' and 'Superion' are trademarks of IonQ, Inc. and are used here solely to designate the target hardware profile.
QECTOR MEGA v2.5.1: High-Performance Quantum Error Correction Decoding Engine Author: Guillaume Lessard, iD01t Productions (ORCID: 0009-0000-3465-3753) Release date: September 20, 2026 Software version: QECTOR MEGA v2.5.1 DOI: 10.5281/zenodo.22863432 What this deposit contains This record archives the extended technical report and the raw benchmark datasets for QECTOR MEGA v2.5.1, a quantum error correction decoding engine. Files: QECTOR_MEGA_v2_5_1_Extended_Zenodo_Report.pdf (39-page extended report: methodology, telemetry tables, threats to validity) and QECTOR_MEGA_v2_5_1_Zenodo.zip (throughput_v11.csv/json with 81 configurations, all_decoders_benchmark_results.json with 18 decoder benchmark entries, maths_physics_production_report.json with 12 mathematical invariant checks, 13 physics entries and 3 OpenCL bit-exactness checks, 8 figures, certification ledger, engineering log, pinned requirements). Measured topologies (as present in the deposited data) The datasets cover 14 topologies: planar surface codes from distance d=3 to d=21, ring codes at n=128, Q70, Q102, Gross [[144,12,12]], Bivariate Bicycle [[288,12]], and regular Gallager ensembles (j=2,k=4) and (j=3,k=6). Note: earlier text mentioned Surface d=25, BB [[400,200]] and Ring n=64; these configurations are NOT present in the deposited datasets and have been removed from this description. Key measured results Peak syndrome extraction throughput: 483,143,722 syndromes/second on Surface d=3 at batch size 1,048,576 (NVIDIA Tesla T4, single run). Decoding: 100.0% faithful recovery (Hc = s mod 2, zero residual violations) on 5/5 configurations at 512 shots each; peak decode throughput 61,927 syndromes/second on Gallager (j=2,k=4). Bit-exactness: 0 mismatches between OpenCL GPU kernels and NumPy references on Surface d=3, 5, 7 (batch 8,192). Mathematical invariants: 12/12 checks passed; physical linear response within 3% relative error for p in [0.001, 0.08]. Measurement caveats. All figures are single-machine measurements (Google Colab, one Tesla T4); headline figures are single runs without quantified uncertainty, and CPU speedup references measured on shared hardware are noisy. Third-party baselines present in the raw JSON (BP-OSD, PyMatching) are not discussed in the report narrative; consult the deposited JSON files for the full picture. Licensing Report, datasets and figures in this record are shared under CC-BY-4.0 (record license). QECTOR MEGA software itself is distributed separately under its own commercial terms (see https://qector.store). Citation Lessard, Guillaume. QECTOR MEGA v2.5.1: High-Performance Quantum Error Correction Decoding Engine. Zenodo, September 2026. doi:10.5281/zenodo.22863432. iD01t Productions.
QECTOR Decoder v3: Syndrome Faithful Decoding, Foundations, Algorithms, and Architecture of a Fifteen Backend Quantum Error Correction Engine QECTOR Decoder v3 is a quantum error correction decoding engine written in Rust with PyO3 Python bindings. It provides fifteen specialized decoding backends unified by a single invariant enforced on every call: syndrome faithfulness, the requirement that H c = s (mod 2) for any correction the engine returns. Scope of this manual This reference manual documents implementation version 1.0.0 of qector decoder v3. Every mathematical statement in it is anchored to source modules and regression tests in the frozen 1.0.0 workspace. Hardware dependent measurements such as latency, throughput, and memory are intentionally excluded from the manual; the methodology for producing and reporting such figures is specified instead, so any future claim is reproducible and auditable. Backend families covered Exact minimum weight perfect matching using Edmonds' blossom algorithmEvent driven Sparse Blossom using radix heap region growthZero allocation Union Find (UF 01)Belief propagation with ordered statistics (BP OSD) for quantum LDPC codesAmbiguity clustering with learned predecodersSpace time and streaming decoding across multiple roundsTwo stage CSS decoding for correlated X and Z noiseCUDA and OpenCL batch kernels, proven bit identical to the CPU reference on tested configurationsA native routing and orchestration layer with a seven tier fallback chain What the manual includes The manual develops the binary field mathematics and stabilizer formalism from first principles, proves the core correctness theorems shared by every backend including syndrome faithfulness, the logical error criterion, and path flipping faithfulness of MWPM, and walks through worked numerical examples including the Steane [[7,1,3]] code, the rotated surface code at distance 3, and a Wilson confidence interval computed by hand. It documents the public API surface, both stable and provisional, the detector error model pipeline, the licensing model and tier enforcement, ecosystem integrations such as a PyMatching compatible shim, Sinter decoders, and a Qiskit plugin, and the testing and validation strategy across correctness, property based, cross decoder equivalence, and GPU bit identity layers. Reproducibility policy Claims in this manual are explicitly scoped: exactness, bit identity, and accuracy statements are attached only to the workloads and configurations on which they were established. No universal performance claim is made anywhere in the document, and prior benchmark artifacts that did not survive a core fingerprint change were formally withdrawn. Appendix D provides the exact reproduction commands, and Appendix C maps every claim to its evidence anchor in the source tree. Keywords quantum error correction, QEC, decoder, MWPM, Union Find, BP OSD, LDPC, qLDPC, surface code, Stim, Sinter, PyMatching, Rust, Python, PyO3, CUDA, batch decoding, reproducible research, benchmarking Author Guillaume Lessard, iD01t Productions, ORCID 0009 0000 3465 3753 Companion document (ground-truth verification campaign, 2026-09-27). PROOFS.pdf, attached to this version, gives the complete re-derived proofs for the decoder theorems of this manual (syndrome fidelity Hc = s, MWPM path-flipping, Union-Find parity algebra and peeling, OSD, AmbiguityCluster, TwoStage, LP optimality certificate), with explicit scope limits and a separate section listing excluded conjectures. See the record errata manifest for retractions applied across the corpus.
QECTOR Decoder Benchmark Datasets & Empirical Reports This repository hosts the evolving collection of reproducible benchmark datasets, JSON measurement artifacts, and empirical performance reports for the QECTOR Decoder v3 platform (Rust/Python quantum error-correction decoder). Each versioned deposit contains environment-stamped, content-hashed JSON artifacts together with the corresponding publication-grade report. All numerical results are fully regenerable from the published wheels and the scripts listed in the reproducibility sections. Scope across versions Code-capacity and circuit-level (Stim rotated_memory_z) evaluations Throughput (shots/s, measure-s/shot), logical error rates with 95 % Wilson intervals, syndrome faithfulness (GF(2) exact check), and CUDA-vs-CPU bit identity Decoder families: FastUnionFind, UnionFind, Blossom (exact MWPM), SparseBlossom, Batch/CPUBatch, BPOSD, HybridCascade, AmbiguityCluster, LookupTable, and CUDABatch (unweighted + DEM-weighted) Hardware provenance, licence-tier disclosure (GPU gated behind Enterprise), and SHA-256 inventories of every backing artifact Version history (selected) v0.6.6 (July 2026) – Workbench Benchmark Master Report: 1 858 decode-timing measurements from 105 runs, six code topologies (Heavy Hex, Repetition, Ring, Rotated Surface, Toric, Unrotated Surface), fixed p = 0.05, distances d = 3–19. Focus on raw latency, harmonic-mean throughput and peak memory. v0.6.8 - Empirical edge-hardware benchmarks. v0.7.0 (August 2026) – Full Empirical Decoder Benchmark Report on the published wheel: nine CPU families + CUDA batch path, circuit-level LER parity with PyMatching 2.4.0, exact syndrome faithfulness, DEM-weighted GPU scaling restoration, and complete artifact inventory (Appendix A). All figures and tables in the accompanying reports are regenerated from the JSON files listed with their SHA-256 hashes; no pre-release numbers are carried forward. Related resources PyPI: qector-decoder-v3 Repository: https://github.com/GuillaumeLessard/qector-decoder Website: https://www.qector.store
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).
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=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.
This technical monograph details the mathematical architecture, algorithmic formulations, exact proofs, and hardware acceleration mechanisms of qector-decoder-v3 v1.0.0. The platform is engineered as an industrial-grade, multi-backend offline decoding suite dedicated to: Threshold benchmarking Quantum simulation routines Large-scale quantum hardware analysis Supported Code Topologies & Frameworks The software incorporates fifteen specialized decoding backend variants optimized to handle complex error structures across diverse geometries: Surface Layouts: Planar, toric, color, and higher-genus surface codes. Hypergraph Topologies: Quantum Low-Density Parity-Check (qLDPC) codes. Formalized Software Optimization Targets The text explicitly formalizes the core mathematical mapping engine: Primal-dual Edmonds linear programming routines. Belief-propagation message-passing updates. Space-time 3D matching lattice models. Neural message-passing edge-readout networks. Bit-packed lookup table index systems. Performance, Verifiability, & Hardware Invariance The library guarantees mathematical and execution stability through rigorous verification paradigms: Syndrome-Faithfulness: Strict mathematical proofs validating Hc≡s(mod2) across all routines. Bit-Identical Invariance: Cross-platform execution parity proving bit-for-bit identity across single-shot CPU, lock-free parallel Rayon, and accelerated GPU hardware batch execution engines (CUDA and OpenCL). Comparative Asymptotics: An exhaustive analytical matrix detailing asymptotic time/space complexities and threshold behaviors under circuit-level and phenomenological noise conditions.