The preparation of quantum Gibbs states is a fundamental challenge in quantum computing, essential for applications ranging from modeling open quantum systems to quantum machine learning. Building on the Meta-Variational Quantum Eigensolver framework proposed by Cervera-Lierta et al.(2021) and a problem driven ansatz design, we introduce two meta-learning algorithms: Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) for efficient thermal state preparation of parametrized Hamiltonians on Noisy Intermediate-Scale Quantum (NISQ) devices. Meta-VQT utilizes a fully quantum ansatz, while NN Meta-VQT integrates a quantum classical hybrid architecture. Both leverage collective optimization over training sets to generalize Gibbs state preparation to unseen parameters. We validate our methods on upto 8-qubit Transverse Field Ising Model and the 2-qubit Heisenberg model with all field terms, demonstrating efficient thermal state generation beyond training data. For larger systems, we show that our meta-learned parameters when combined with appropriately designed ansatz serve as warm start initializations, significantly outperforming random initializations in the optimization tasks. Furthermore, a 3- qubit Kitaev ring example showcases our algorithm's effectiveness across finite-temperature crossover regimes. Finally, we apply our algorithms to train a Quantum Boltzmann Machine (QBM) on a 2-qubit Heisenberg model with all field terms, achieving enhanced training efficiency, improved Gibbs state accuracy, and a 30-fold runtime speedup over existing techniques such as variational quantum imaginary time (VarQITE)-based QBM highlighting the scalability and practicality of meta-algorithm-based QBMs.

翻译：量子吉布斯态的制备是量子计算中的一项基础性挑战，对于从开放量子系统建模到量子机器学习等应用至关重要。基于 Cervera-Lierta 等人（2021）提出的元变分量子本征求解器框架以及问题驱动的拟设设计，我们引入了两种元学习算法：元变分量子热化器（Meta-VQT）和神经网络元变分量子热化器（NN-Meta VQT），用于在含噪声中等规模量子（NISQ）设备上高效制备参数化哈密顿量的热态。Meta-VQT 采用全量子拟设，而 NN-Meta VQT 则集成了量子-经典混合架构。两者均利用对训练集的集体优化，将吉布斯态制备推广至未见过的参数。我们在最多 8 量子位的横场伊辛模型和包含所有场项的 2 量子位海森堡模型上验证了我们的方法，证明了其能够在训练数据之外高效生成热态。对于更大规模的系统，我们表明，将元学习得到的参数与适当设计的拟设相结合，可以作为优化任务中的热启动初始化，其性能显著优于随机初始化。此外，一个 3 量子位的 Kitaev 环示例展示了我们的算法在有限温度交叉区域的有效性。最后，我们将算法应用于在包含所有场项的 2 量子位海森堡模型上训练量子玻尔兹曼机（QBM），实现了训练效率的提升、吉布斯态精度的提高，以及相较于基于变分量子虚时（VarQITE）的 QBM 等现有技术高达 30 倍的运行加速，突显了基于元算法的 QBM 的可扩展性与实用性。