PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization

2025-09-25

AI Summary

To address the prohibitively high quantum resource consumption and incompatibility with standard backpropagation in variational quantum algorithms (VQAs) for large-scale tasks—stemming from the no-cloning theorem—this work introduces the first continuous dynamical modeling of VQA parameter optimization as a nonlinear partial differential equation (PDE) system. We propose a classical-side, multi-step parameter evolution prediction framework grounded in physics-informed neural networks (PINNs), which learns the optimization manifold from sparse quantum trajectory data without requiring real-time quantum circuit evaluations. On a 40-qubit task, our method achieves up to 30× faster training and reduces quantum resource usage by 90%, while preserving original accuracy. The core contributions are: (i) establishing a continuous dynamical systems characterization of VQA optimization; and (ii) pioneering the integration of PINNs with quantum trajectory modeling, thereby significantly alleviating the quantum-classical co-training resource bottleneck in the NISQ era.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Variational quantum algorithms (VQAs) are leading strategies to reach practical utilities of near-term quantum devices. However, the no-cloning theorem in quantum mechanics precludes standard backpropagation, leading to prohibitive quantum resource costs when applying VQAs to large-scale tasks. To address this challenge, we reformulate the training dynamics of VQAs as a nonlinear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.

Problem

• Reducing prohibitive quantum resource costs in large-scale variational quantum algorithms
• Overcoming no-cloning theorem limitations that prevent standard backpropagation in VQAs
• Accelerating quantum optimization tasks while maintaining competitive solution accuracy

Innovation

• Reformulates VQA training as PDE dynamics
• Uses physics-informed neural networks for prediction
• Reduces quantum resource costs by 90%