Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms

2025-01-10

AI Summary

Variational quantum algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices suffer from sensitivity to initial parameters and slow convergence. Method: We propose the first quantum-model-agnostic meta-learning framework, wherein a classical neural network (the Learner) generates initialization parameters for parameterized quantum circuits (PQCs), decoupling meta-learning from quantum optimization. The Learner is pre-trained via Model-Agnostic Meta-Learning (MAML) and then frozen; adaptation to new Hamiltonians requires only a few PQC gradient updates. Contribution/Results: Evaluated on Heisenberg XYZ Hamiltonian optimization and distribution mapping tasks, our method achieves 3–5× faster convergence compared to random initialization, while maintaining high adaptability to unseen problems. This work pioneers the integration of MAML into quantum optimization, establishing a new paradigm for few-shot, robust VQAs on NISQ hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

In the Noisy Intermediate-Scale Quantum (NISQ) era, using variational quantum algorithms (VQAs) to solve optimization problems has become a key application. However, these algorithms face significant challenges, such as choosing an effective initial set of parameters and the limited quantum processing time that restricts the number of optimization iterations. In this study, we introduce a new framework for optimizing parameterized quantum circuits (PQCs) that employs a classical optimizer, inspired by Model-Agnostic Meta-Learning (MAML) technique. This approach aim to achieve better parameter initialization that ensures fast convergence. Our framework features a classical neural network, called Learner}, which interacts with a PQC using the output of Learner as an initial parameter. During the pre-training phase, Learner is trained with a meta-objective based on the quantum circuit cost function. In the adaptation phase, the framework requires only a few PQC updates to converge to a more accurate value, while the learner remains unchanged. This method is highly adaptable and is effectively extended to various Hamiltonian optimization problems. We validate our approach through experiments, including distribution function mapping and optimization of the Heisenberg XYZ Hamiltonian. The result implies that the Learner successfully estimates initial parameters that generalize across the problem space, enabling fast adaptation.

Problem

• Variational Quantum Algorithms
• Initial Parameter Setting
• Optimization within Quantum Computing Time Limits

Innovation

• Q-MAML
• Variational Quantum Algorithms
• Model-Agnostic Meta-Learning