Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study

Quantum Physics arXiv:2609.13505 (quant-ph) [Submitted on 11 Sep 2026] Title:Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study Authors:Kip Nieman, Daniel Koch View a PDF of the paper titled Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study, by Kip Nieman and Daniel Koch View PDF HTML (experimental) Abstract:Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is well-positioned for combinatorial optimization and is particularly promising for Quadratic Unconstrained Binary Optimization (QUBO) problems. QAA is appealing due to its ability to drive the quantum system to a target state, yielding the globally optimal solution with probability over $90$+%. However, realizing QAA for application-scale optimization currently exceeds quantum hardware capacity, which is further compounded by unresolved algorithmic challenges regarding the choice of free parameters. In this study, we address these issues by utilizing a realistic traffic flow QUBO problem to investigate the implementation of QAA as a heuristic solver. Specifically, allowing the diffusion operator parameter to take non-$\pi$ values expands the capabilities of QAA. This unlocks a new multiple-shot, low-iteration strategy that aims for a high cumulative probability rather than maximizing the probability of a single basis state. Using $25$-qubit simulations, our results demonstrate that heuristic QAA addresses two of the main challenges cited in previous studies. Firstly, heuristic QAA works even at a single iteration, reducing circuit depth by orders of magnitude compared to standard QAA. And secondly, we show that the problem-dependent parameters necessary for reaching optimal algorithmic performance can be reliably approximated with minimal upfront classical computing overhead. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.13505 [quant-ph] (or arXiv:2609.13505v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.13505 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kip Nieman [view email] [v1] Fri, 11 Sep 2026 20:11:46 UTC (10,412 KB) Full-text links: Access Paper: View a PDF of the paper titled Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study, by Kip Nieman and Daniel KochView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)