A Digital Spreading Framework for Quantum Expectation Computation Without Rotation Gates or Arithmetic Circuits

Quantum Physics [Submitted on 7 Apr 2026] A Digital Spreading Framework for Quantum Expectation Computation Without Rotation Gates or Arithmetic Circuits Yu-Ting Kao, Yeong-Jar Chang In the pursuit of quantum advantage for financial engineering, researchers face a critical dilemma: analog rotation gates suffer from inherent 'sine-to-square' biases and error magnification, while digital arithmetic circuits (e.g., WeightedAdder) incur prohibitive quadratic complexity that exceeds NISQ capabilities. This study introduces Digital Spreading (DS), a fully digital quantum computing framework designed to resolve this trade-off. DS overcomes these limitations by utilizing a pruned Cuccaro ripple-carry architecture that avoids costly multiplication and eliminates rotation gates entirely. The proposed circuit employs integer comparison operations on superposed quantum states, mapping multi-qubit outcomes onto the probability of a single target qubit. Experiments based on a random walk model for option pricing demonstrate that DS achieves floating-point precision with a relative error as low as 0.0001%, outperforming JP Morgan's rotation-based method (1.43%), as well as ITRI's analog calibration (1.43%) and digital calibration approaches (19.14%). Overall, DS provides a compact, robust, and accurate framework for quantum weighted-average computation. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.05452 [quant-ph]   (or arXiv:2604.05452v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.05452 Focus to learn more Submission history From: Yu-Ting Kao [view email] [v1] Tue, 7 Apr 2026 05:37:31 UTC (658 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)