Deterministic Reasoning for Quantum Error Correction: A Proof-Carrying Control and Compression Framework

This work introduces QEC, a deterministic, replay-safe reasoning system for quantum error correction and invariant-driven computation.

Unlike conventional adaptive systems that rely on stochastic exploration, QEC operates as a deterministic reasoning layer over system evolution, producing proof-carrying state transitions that are fully reproducible and verifiable.

The system replaces probabilistic optimization with a structured pipeline of invariant detection, deterministic control, memory accumulation, governance, validation, repair reasoning, and invariant-preserving compression. Each stage produces canonical, hash-stable artifacts, ensuring that identical inputs yield byte-identical outputs across environments.

QEC reframes failure as a structural phenomenon ("dark states") and introduces deterministic repair through symmetry breaking, validated via counterfactual replay. The system further demonstrates that reasoning itself can be compressed into minimal canonical forms without loss of replay fidelity.

Empirical runs over QLDPC Tanner graph simulations demonstrate zero hash divergence across independent executions and compact proof artifacts (~2–5 KB), supporting the feasibility of deterministic reasoning with proof in complex systems.

This work establishes a new paradigm:

execution → reasoning → proof