Quantum Error Mitigation Strategies for Variational PDE-Constrained Circuits on Noisy Hardware

Quantum Physics [Submitted on 11 Apr 2026] Quantum Error Mitigation Strategies for Variational PDE-Constrained Circuits on Noisy Hardware Prasad Nimantha Madusanka Ukwatta Hewage, Midhun Chakkravarthy, Ruvan Kumara Abeysekara Variational quantum circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence. We present a systematic study of three noise channels; depolarizing, amplitude damping, and bit-flip on VQCs constrained by PDE residual loss functions for the heat equation, Burgers' equation, and the Saint-Venant shallow water equations. We benchmark three error mitigation strategies: zero-noise extrapolation (ZNE) via Richardson polynomial fitting, probabilistic error cancellation (PEC), and measurement error mitigation through inverse confusion matrices. Our numerical experiments on 6-qubit, 4-layer circuits demonstrate that ZNE reduces absolute error by 82-96% at low noise (p = 0.001), with effectiveness degrading gracefully at higher noise strengths. We prove analytically and confirm numerically that physics-constrained circuits exhibit inherent noise resilience: at p = 0.01, constrained circuits maintain 25-47% higher fidelity than unconstrained counterparts, with the advantage scaling with PDE complexity. PEC provides near-exact correction at low gate counts but incurs exponential sampling overhead, rendering it impractical beyond ~60 gates at p >= 0.02. Error budget decomposition reveals that systematic errors dominate at all noise levels (43-58%), while the PDE residual component grows from ~10% to ~31% as noise increases, indicating that physics constraints absorb noise through structured gradient information. These results establish practical guidelines for deploying variational PDE solvers on NISQ hardware. Comments: 15 pages, 6 figures, 5 tables Github Repo: git@github.com:nimanpra/quantum_error_mitigation_strategies.git Subjects: Quantum Physics (quant-ph) MSC classes: 81Q80, 65M99, 81P68 Cite as: arXiv:2604.10099 [quant-ph]   (or arXiv:2604.10099v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.10099 Focus to learn more Submission history From: Prasad Nimantha Madusanka Ukwatta Hewage [view email] [v1] Sat, 11 Apr 2026 08:45:08 UTC (71 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)