Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer
Summarize this article with:
Quantum Physics arXiv:2602.07097 (quant-ph) [Submitted on 6 Feb 2026] Title:Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer Authors:Tayyab Ali View a PDF of the paper titled Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer, by Tayyab Ali View PDF Abstract:The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which provides a high dimensional infinite linear system corresponding to a finite nonlinear system, as an indirect way of solving nonlinear systems using current quantum computers. We provide an efficient data access model to load this infinite linear representation of the nonlinear system, upto truncation order $N$, on a quantum computer by decomposing the Hamiltonian into the weighted sum of non-unitary operators, namely the Sigma basis. We have shown that the Sigma basis provides an exponential reduction in the number of decomposition terms compared to the traditional decomposition, which is usually done in a linear combination of Pauli operators. Once the Hamiltonian is decomposed, we then use the concept of unitary completion to construct the circuit for the implementation of each weighted tensor product component $\mathcal{H}_{j}$ of the decomposition. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.07097 [quant-ph] (or arXiv:2602.07097v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.07097 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tayyab Ali [view email] [v1] Fri, 6 Feb 2026 14:56:39 UTC (652 KB) Full-text links: Access Paper: View a PDF of the paper titled Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer, by Tayyab AliView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)