Designing tight frames for quantum computing

Quantum Physics arXiv:2607.27247 (quant-ph) [Submitted on 28 Jul 2026] Title:Designing tight frames for quantum computing Authors:Luis Quezada View a PDF of the paper titled Designing tight frames for quantum computing, by Luis Quezada View PDF HTML (experimental) Abstract:The aim of this thesis is to explore the implementation of a special kind of quantum measurements, so called harmonic tight frames. To achieve this goal, representation theory is addressed, emphasizing its construction from irreducible representations and the relations they satisfy. These tools simplify the study due to the existence of symmetries, leading to the concept of group frames, defined as orbits under the unitary action of a group and characterized by their symmetry groups. Among the various groups, the simplest are the abelian ones, giving rise to harmonic frames, which are analyzed through the classification theorem of abelian groups and the characters of their irreducible representations. In the quantum mechanics context, the frame elements can be interpreted as pure states of a system. Therefore, the necessary and sufficient conditions for separability are explored, as separable states are easier to implement due to their local nature. Alternatively, when viewing frames as measurements, the concept of POVMs and Naimark's theorem are studied as key tools for designing measurements in quantum computers. Using this knowledge, a characterization of the harmonic frames is given from the abelian group structure theorem, which allows obtaining a necessary and sufficient condition for their separability. The conditions of maximum entanglement of these states for bipartite systems are also studied, obtaining a necessary condition on the dimensions of the subsystems. Finally, a quantum circuit is obtained that allows implementing the harmonic frames associated to cyclic groups as POVMs using a Fourier matrix and a permutation matrix. We conclude by giving simple examples where the results are applied to quantum computers and proposing future avenues of research that could serve to improve the circuit design and extend it to the case of all harmonic frames. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.27247 [quant-ph] (or arXiv:2607.27247v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.27247 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Luis Quezada [view email] [v1] Tue, 28 Jul 2026 03:43:06 UTC (493 KB) Full-text links: Access Paper: View a PDF of the paper titled Designing tight frames for quantum computing, by Luis QuezadaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)