qector-decoder-v3: A High-Performance, Multi-Backend Software Architecture for Quantum Error Correction

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 \(Hc ≡ s 2\) 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.