The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models

[2608.14691] The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14691 (cs) [Submitted on 7 Aug 2026] Title: The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models Authors: Ahmed Nebli , Hadi Saadatdoorabi , Christopher Keibel , Kevin Yam View a PDF of the paper titled The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models, by Ahmed Nebli and 3 other authors View PDF HTML (experimental) Abstract: Sequence models are conventionally distinguished by their backbone, the mechanism that routes information across positions, such as attention or recurrence. This paper varies a choice that is prior to the backbone and shared by nearly all current models: the \emph{substrate}, the number system in which the hidden state is represented together with the form of the map from state to prediction. The prevailing substrate is a real-valued state with an affine--softmax readout; we study a complex-valued alternative drawn from the mathematics of quantum theory, in which information is carried by the phases of the state and scores are quadratic Born forms. Prior work proved an idealized version of this substrate representationally stronger than any real model with a linear readout; we ask whether it also trains faster. Relaxing the two properties that block deployment, exact unitarity and the Born vocabulary readout, we instantiate it in the Mamba state-space model and an attention-based Transformer. At 253M parameters, matched to within $0.02\%$ and trained under one fixed protocol on three byte-level corpora, the complex models reach every measured validation loss in approximately one third (state-space) and one half (attention) of the optimization steps of their real counterparts. The two backbones then diverge. Once the learning-rate warmup ends, the state-space advantage continues to widen, from $0.321$ to $0.354$ bits per character on OpenWebText and from $0.368$ to $0.396$ on FineWeb, which an artifact of the warmup ramp would not do; the attention advantage instead decays toward zero on every corpus, and is therefore an effect of early training. Subjects: Machine Learning (cs.LG) ; Quantum Physics (quant-ph) Cite as: arXiv:2608.14691 [cs.LG] (or arXiv:2608.14691v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14691 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ahmed Nebli [ view email ] [v1] Fri, 7 Aug 2026 15:12:36 UTC (277 KB) Full-text links: Access Paper: View a PDF of the paper titled The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models, by Ahmed Nebli and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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