Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction

Quantum Physics [Submitted on 26 Mar 2026] Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction Hikaru Wakaura We present Catalytic Quantum Error Correction (CQEC), a quantum state recovery protocol based on the arbitrary amplification of coherence in catalytic covariant transformations. Unlike conventional quantum error correction, CQEC requires knowledge of the target state and multiple noisy copies, but operates without an error threshold: recovery succeeds whenever the coherent modes of the target state are contained within those of the noisy state (mode inclusion), regardless of the noise magnitude. A reusable catalyst state mediates the transformation and its reduced state is preserved exactly after each cycle (correlated catalysis). We validate CQEC numerically across four quantum algorithms -- qDRIFT, quantum Kolmogorov--Arnold networks, control-free phase estimation, and Regev factoring -- and a tree tensor network cryptographic protocol, under dephasing, depolarizing, and combined noise. In the asymptotic (infinite-copy) limit, CQEC recovers the known algorithmic output state from fidelity F = 0.07 to F > 0.999 across 200 configurations; at finite copy number n, the fidelity gap scales as 1 - F \leq O(1/\sqrt{n}). We compare with Steane and surface codes under their respectively different operational assumptions. Our results establish coherence resource theory as a complementary foundation for quantum state recovery. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.25774 [quant-ph]   (or arXiv:2603.25774v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.25774 Focus to learn more Submission history From: Hikaru Wakaura [view email] [v1] Thu, 26 Mar 2026 12:03:20 UTC (187 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)