Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware
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Quantum Physics arXiv:2512.23817 (quant-ph) [Submitted on 29 Dec 2025] Title:Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware Authors:Seyed Mohamad Ali Tousi, Adib Bazgir, Yuwen Zhang, G. N. DeSouza View a PDF of the paper titled Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware, by Seyed Mohamad Ali Tousi and 3 other authors View PDF HTML (experimental) Abstract:We present a hybrid quantum-classical framework augmented with learned error mitigation for solving the viscous Burgers equation on noisy intermediate-scale quantum (NISQ) hardware. Using the Cole-Hopf transformation, the nonlinear Burgers equation is mapped to a diffusion equation, discretized on uniform grids, and encoded into a quantum state whose time evolution is approximated via Trotterized nearest-neighbor circuits implemented in Qiskit. Quantum simulations are executed on noisy Aer backends and IBM superconducting quantum devices and are benchmarked against high-accuracy classical solutions obtained using a Krylov-based solver applied to the corresponding discretized Hamiltonian. From measured quantum amplitudes, we reconstruct the velocity field and evaluate physical and numerical diagnostics, including the L2 error, shock location, and dissipation rate, both with and without zero-noise extrapolation (ZNE). To enable data-driven error mitigation, we construct a large parametric dataset by sweeping viscosity, time step, grid resolution, and boundary conditions, producing matched tuples of noisy, ZNE-corrected, hardware, and classical solutions together with detailed circuit metadata. Leveraging this dataset, we train an attention-based graph neural network that incorporates circuit structure, light-cone information, global circuit parameters, and noisy quantum outputs to predict error-mitigated solutions. Across a wide range of parameters, the learned model consistently reduces the discrepancy between quantum and classical solutions beyond what is achieved by ZNE alone. We discuss extensions of this approach to higher-dimensional Burgers systems and more general quantum partial differential equation solvers, highlighting learned error mitigation as a promising complement to physics-based noise reduction techniques on NISQ devices. Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2512.23817 [quant-ph] (or arXiv:2512.23817v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.23817 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Seyed Mohamad Ali Tousi [view email] [v1] Mon, 29 Dec 2025 19:23:20 UTC (5,025 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware, by Seyed Mohamad Ali Tousi and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.AI cs.LG References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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