Optimization of the HHL Algorithm
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Quantum Physics arXiv:2603.15756 (quant-ph) [Submitted on 16 Mar 2026] Title:Optimization of the HHL Algorithm Authors:Dhruv Sood, Nilmani Mathur, Vikram Tripathi View a PDF of the paper titled Optimization of the HHL Algorithm, by Dhruv Sood and 2 other authors View PDF HTML (experimental) Abstract:The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work, we investigate the practical implementation and optimisation of the HHL algorithm with a focus on improving its performance on near-term quantum simulators. After outlining the algorithm, we examine two optimisation strategies aimed at improving fidelity and scalability: Suzuki-Trotter decomposition of the Hamiltonian evolution operator and a block-encoding approach that embeds the problem matrix into a larger unitary operator. The performance of these methods is evaluated through simulations on matrices with varying sparsity, including diagonal, tridiagonal, moderately dense, and fully dense cases. Our results show that while HHL achieves near-ideal fidelity for highly structured matrices, performance degrades as sparsity decreases due to the increasing cost of Hamiltonian simulation and reduced post-selection probability due to higher condition number. Block encoding is found to provide improved fidelity for moderately dense matrices, whereas Trotterisation offers a qubit-efficient approach for sparse systems. These results highlight the importance of matrix structure in determining the practical efficiency of HHL and inform future implementations that combine algorithmic optimisation with hardware-aware design. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat) Report number: TIFR/TH/26-10 Cite as: arXiv:2603.15756 [quant-ph] (or arXiv:2603.15756v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.15756 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Dhruv Sood [view email] [v1] Mon, 16 Mar 2026 18:00:14 UTC (464 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimization of the HHL Algorithm, by Dhruv Sood and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: hep-lat 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?)