A SWAP-free Framework for QAOA

Quantum Physics arXiv:2604.25058 (quant-ph) [Submitted on 27 Apr 2026] Title:A SWAP-free Framework for QAOA Authors:Thiago Assis, Pedro Baptista, Laila Lopes, Diego Ferreira, Gabriel Coutinho View a PDF of the paper titled A SWAP-free Framework for QAOA, by Thiago Assis and 4 other authors View PDF HTML (experimental) Abstract:The performance of the Quantum Approximate Optimization Algorithm (QAOA) on noisy intermediate-scale quantum (NISQ) devices is strongly limited by sparse qubit connectivity. When interactions required by QAOA Hamiltonians are not aligned to the hardware topology, transpilation introduces SWAP gates, increasing circuit depth and noise. We propose a SWAP-free QAOA framework based on modifying the cost Hamiltonian so that it can be implemented natively on the hardware. We formulate this as a mixed-integer semidefinite program (MISDP) that selects a hardware-compatible approximation of the original cost matrix and optimizes the allocation of logical variables to physical qubits. We prove that the associated decision problem is NP-complete and derive theoretical guarantees relating the MISDP objective to the loss in the original optimization problem through the Lovász number of the hardware graph. Since solving MISDPs is practical only for small instances, we introduce heuristics based on spectral properties of the problem matrix and hardware graph. Our experiments on a cardinality-constrained quadratic optimization model for index tracking show competitive performance against a baseline representing ideal QAOA under SWAP-induced noise. These results indicate that, on sparse NISQ architectures, a hardware-aware approximation of the objective may be more effective than an exact but heavily transpiled Hamiltonian implementation. Comments: Subjects: Quantum Physics (quant-ph); Combinatorics (math.CO) Cite as: arXiv:2604.25058 [quant-ph] (or arXiv:2604.25058v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.25058 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pedro Vinícius Ferreira Baptista [view email] [v1] Mon, 27 Apr 2026 23:13:20 UTC (1,083 KB) Full-text links: Access Paper: View a PDF of the paper titled A SWAP-free Framework for QAOA, by Thiago Assis and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math.CO 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?)