Dyadic-Order Quantum Fractional Transforms: Circuit Constructions and Applications to Hartley and Cosine Transform Families

Quantum Physics [Submitted on 10 Apr 2026] Dyadic-Order Quantum Fractional Transforms: Circuit Constructions and Applications to Hartley and Cosine Transform Families Matheus J. A. Oliveira, Israel F. Araujo, José R. de Oliveira Neto, Juliano B. Lima This paper presents a generalized circuit framework for constructing Shih-type fractionalizations of unitary operators of dyadic order, i.e., operators U satisfying U^{2^n}=I. Building upon the architecture of the quantum fractional Fourier transform (QFrFT), we show that fractionalization can be implemented coherently as a weighted superposition of integer powers, \sum_k c_k(\alpha)U^k, where the coefficients are generated through an ancilla-domain quantum Fourier transform and a diagonal phase modulation. Under the assumption that controlled implementations of the required powers of U are available, the resulting circuit yields a parameterized family of operators that interpolates the integer powers of U and satisfies the additive property of fractional transforms. As concrete applications, we derive explicit quantum circuit realizations of the quantum fractional Hartley transform (QFrHT) and of the fractional cosine-transform families associated with Types~I and~IV. These constructions demonstrate the versatility of the proposed dyadic-order fractionalization framework for structured operators arising in quantum signal processing. Comments: 16 pages 8 figures Subjects: Quantum Physics (quant-ph); Signal Processing (eess.SP) Cite as: arXiv:2604.09295 [quant-ph]   (or arXiv:2604.09295v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.09295 Focus to learn more Submission history From: Matheus Oliveira [view email] [v1] Fri, 10 Apr 2026 13:04:55 UTC (3,170 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: eess eess.SP 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?)