Hermitian Matrix Function Synthesis without Block-Encoding

Quantum Physics arXiv:2512.18249 (quant-ph) [Submitted on 20 Dec 2025] Title:Hermitian Matrix Function Synthesis without Block-Encoding Authors:Anuradha Mahasinghe, Kaushika De Silva, Xavier Cadet, Peter Chin, Frederic Cadet, Jingbo Wang View a PDF of the paper titled Hermitian Matrix Function Synthesis without Block-Encoding, by Anuradha Mahasinghe and 4 other authors View PDF HTML (experimental) Abstract:Implementing arbitrary functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine learning kernels, and other advance quantum algorithms. Existing state-of-the-art techniques, including Qubitization, Quantum Singular Value Transformation (QSVT), and Quantum Signal Processing (QSP), rely heavily on block-encoding the Hermitian matrix. These methods are often constrained by the complexity of preparing the block-encoded state, the overhead associated with the required ancillary qubits, or the challenging problem of angle synthesis for the polynomial's phase factors, which limits the achievable circuit depth and overall efficiency. In this work, we propose a novel and resource-efficient approach to implement arbitrary polynomials of a Hermitian matrix, by leveraging the Generalized Quantum Signal Processing (GQSP) framework. Our method circumvents the need for block-encoding by expressing the target Hermitian matrix as a symmetric combination of unitary conjugates, enabling polynomial synthesis via GQSP circuits applied to each unitary component. We derive closed-form expressions for symmetric polynomial expansions and demonstrate how linear combinations of GQSP circuits can realize the desired transformation. This approach reduces resource overhead, and opens new pathways for quantum algorithm design for functions of Hermitian matrices. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.18249 [quant-ph] (or arXiv:2512.18249v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.18249 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jingbo Wang [view email] [v1] Sat, 20 Dec 2025 07:22:04 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Hermitian Matrix Function Synthesis without Block-Encoding, by Anuradha Mahasinghe and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)