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.

翻译：在噪声中等规模量子（NISQ）时代，利用变分量子算法（VQAs）解决优化问题已成为关键应用。然而，这些算法面临显著挑战，例如选择有效的初始参数集，以及有限的量子处理时间限制了优化迭代次数。本研究提出一种优化参数化量子电路（PQCs）的新框架，该框架采用受模型无关元学习（MAML）技术启发的经典优化器。该方法旨在获得能确保快速收敛的更好参数初始化。我们的框架包含一个称为“学习器”的经典神经网络，该网络与PQC交互，并将学习器的输出作为初始参数。在预训练阶段，学习器基于量子电路成本函数的元目标进行训练。在适应阶段，该框架仅需少量PQC更新即可收敛到更精确值，而学习器保持不变。此方法具有高度适应性，并能有效扩展到各类哈密顿量优化问题。我们通过包括分布函数映射和海森堡XYZ哈密顿量优化在内的实验验证了所提方法。结果表明，学习器能成功估计在问题空间中泛化的初始参数，从而实现快速适应。