# Meta-learning of Gibbs states for many-body Hamiltonians with applications to Quantum Boltzmann Machines

arXiv: https://arxiv.org/abs/2507.16373 · HTML: https://mlsanity.com/paper/2507.16373/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 65 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm](https://mlsanity.com/paper/1910.02071/) (2019)
- [Optimizing quantum heuristics with meta-learning](https://mlsanity.com/paper/1908.03185/) (2019)
- [Generative training of quantum Boltzmann machines with hidden units](https://mlsanity.com/paper/1905.09902/) (2019)
- [Quantum Speed-ups for Semidefinite Programming](https://mlsanity.com/paper/1609.05537/) (2016)
- [Variational quantum Gibbs state preparation with a truncated Taylor series](https://mlsanity.com/paper/2005.08797/) (2020)
- [Measuring Quantum Entropy](https://mlsanity.com/paper/1711.00814/) (2017)
- [Learning To Optimize Quantum Neural Network Without Gradients](https://mlsanity.com/paper/2304.07442/) (2023)
- [Enhancing variational quantum algorithms by balancing training on classical and quantum hardware](https://mlsanity.com/paper/2503.16361/) (2025)

## Built on by (most cited first, 3 of 3)

- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [Structured quantum learning via em algorithm for Boltzmann machines](https://mlsanity.com/paper/2507.21569/) (2025)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)

## Abstract (arXiv)

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.