Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA

Quantum Physics arXiv:2606.28536 (quant-ph) [Submitted on 26 Jun 2026] Title:Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA Authors:Stefano Cipolla, Fabio Durastante View a PDF of the paper titled Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA, by Stefano Cipolla and 1 other authors View PDF HTML (experimental) Abstract:Combinatorial optimization is a leading target for quantum algorithms, but finite-depth QAOA can suffer from strong diabatic errors when the interpolation Hamiltonian has small, or exponentially small, spectral gaps. We propose a Pauli-sparse counterdiabatic extension of linear-ramp QAOA based on the regularised adiabatic gauge potential \[ \bigl(\mathcal L_H^2+\eta I\bigr)A_\lambda^{(\eta)} = -\mathrm{i}\mathcal L_H(\partial_\lambda H), \qquad \mathcal L_H(X)=[H,X]. \] Instead of computing a dense AGP, we solve this equation approximately by an inexact conjugate-gradient method in Pauli coordinates, truncating the Pauli expansion during the iteration to obtain a gate-budget-aware set of implementable rotations. The selected support is then improved by a Galerkin refit and certified by an a posteriori residual bound. The regularization parameter \(\eta\) acts as an energy-resolution scale: it suppresses transitions below \(\sqrt{\eta}\) while retaining larger-gap transitions. Thus, the method can avoid resolving exponentially small splittings inside a low-energy solution manifold while reducing leakage away from it. Numerical experiments on Ferromagnetic Chain (FC) and perturbed FC--MaxCut/MarketSplit instances show that the resulting LR-CD-QAOA ansatz improves approximation ratios over the uncorrected linear ramp, especially in regimes where LR-QAOA remains far from the optimum. Overall, the proposed regularized LR-CD-QAOA framework substantially broadens the practical applicability of QAOA to QUBO optimization by improving its robustness across heterogeneous problem landscapes, including instances with near-degenerate low-energy structures and small spectral gaps. Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Cite as: arXiv:2606.28536 [quant-ph] (or arXiv:2606.28536v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.28536 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Stefano Cipolla [view email] [v1] Fri, 26 Jun 2026 18:41:15 UTC (1,188 KB) Full-text links: Access Paper: View a PDF of the paper titled Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA, by Stefano Cipolla and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: math math.OC 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?)