The PID Controller Strikes Back: Classical Controller Helps Mitigate Barren Plateaus in Noisy Variational Quantum Circuits

Quantum Physics arXiv:2511.14820 (quant-ph) [Submitted on 18 Nov 2025] Title:The PID Controller Strikes Back: Classical Controller Helps Mitigate Barren Plateaus in Noisy Variational Quantum Circuits Authors:Zhehao Yi, Rahul Bhadani View a PDF of the paper titled The PID Controller Strikes Back: Classical Controller Helps Mitigate Barren Plateaus in Noisy Variational Quantum Circuits, by Zhehao Yi and Rahul Bhadani View PDF HTML (experimental) Abstract:Variational quantum algorithms (VQAs) combine the advantages of classical optimization and quantum computation, making them one of the most promising approaches in the Noisy Intermediate-Scale Quantum (NISQ) era. However, when optimized using gradient descent, VQAs often suffer from the vanishing gradient problem, commonly known as the barren plateau. Various methods have been proposed to mitigate this issue. In this work, we propose a hybrid approach that integrates a classical proportional-integral-derivative (PID) controller with a neural network to update the parameters of variational quantum circuits. We refer to this method as NPID, which aims to mitigate the barren plateau. The proposed algorithm is tested on randomly generated quantum input states and random quantum circuits with parametric noise to evaluate its universality, and additional simulations are conducted under different noise rates to examine its robustness. The effectiveness of the proposed method is evaluated based on its convergence speed toward the target cost value. Simulation results show that NPID achieves a convergence efficiency 2-9 times higher than NEQP and QV, with performance fluctuations averaging only 4.45% across different noise levels. These results highlight the potential of integrating classical control theory into quantum optimization, providing a new perspective for improving the trainability and stability of variational quantum algorithms. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.14820 [quant-ph] (or arXiv:2511.14820v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.14820 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zhehao Yi [view email] [v1] Tue, 18 Nov 2025 14:55:42 UTC (3,684 KB) Full-text links: Access Paper: View a PDF of the paper titled The PID Controller Strikes Back: Classical Controller Helps Mitigate Barren Plateaus in Noisy Variational Quantum Circuits, by Zhehao Yi and Rahul BhadaniView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)