Constructive realization of self-referential prediction limits in quantum control: Resource bounds and Gödel-safe architectures

[2608.04779] Constructive realization of self-referential prediction limits in quantum control: Resource bounds and Gödel-safe architectures Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2608.04779 (quant-ph) [Submitted on 5 Aug 2026] Title: Constructive realization of self-referential prediction limits in quantum control: Resource bounds and Gödel-safe architectures Authors: Salman Sajad Wani , Álvaro Perales-Eceiza , Saif Al-Kuwari , Mir Faizal View PDF HTML (experimental) Abstract: Programmable quantum control systems increasingly rely on predictive modules for certification, real-time feedback, and autonomous decision-making. This development raises a fundamental question: can self-analyzing quantum platforms universally predict their own experimental outcomes? Wolpert formalized a general impossibility of universal self-prediction. Here we translate that limitation into an explicit laboratory obstruction that can be realized with finite resources. We consider settings with programmable quantum control in which predictors can be embedded as subroutines within the experiments they analyze. Our diagonal construction uses Kleene's recursion theorem to transform any deterministic bounded-time predictor into a reversible protocol encoding its own specification. The resulting protocol invokes the predictor on that specification and deterministically produces a classical pointer record that contradicts the forecast. For efficient predictors, the compilation has polynomial overhead and admits concrete physical realizations as a fault-tolerant quantum circuit and as a minimal Mach-Zehnder interferometer. These realizations connect computability-theoretic self-reference to programmable quantum hardware. We also introduce and formally define Gödel-safe architectures. These architectures block the forbidden causal path from the protocol description to an actuator that can affect the pointer during the same run. We analyze their implications for real-time quantum error correction, including the resulting expressiveness trade-offs. As quantum control loops grow in computational expressiveness, the limits of self-reference cease to be mere mathematical abstractions and become explicit engineering constraints for the reliable operation of autonomous quantum technologies. Comments: 22 pages, 2 figures, supplementary material Subjects: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph) Cite as: arXiv:2608.04779 [quant-ph] (or arXiv:2608.04779v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.04779 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Quantum Sci. Technol. 11 045001 (2026) Related DOI : https://doi.org/10.1088/2058-9565/ae94a3 Focus to learn more DOI(s) linking to related resources Submission history From: Alvaro Perales Eceiza [ view email ] [v1] Wed, 5 Aug 2026 12:46:41 UTC (1,585 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-08 Change to browse by: math math-ph math.MP 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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