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

2025-07-22

AI Summary

To address the low efficiency and poor generalizability of preparing quantum Gibbs states for parameterized many-body Hamiltonians on NISQ devices, this work pioneers the integration of meta-learning into quantum thermal state preparation, proposing two algorithms: Meta-VQT and NN-Meta-VQT. Our approach synergistically combines variational quantum imaginary-time evolution (VarQITE), a meta-variational eigensolver framework, and problem-driven ansatz design, supporting both fully quantum and quantum-classical hybrid architectures; it further leverages collective optimization and neural-network-assisted initialization. Validated on an 8-qubit system, the algorithms demonstrate cross-temperature and cross-model-parameter transferability, enabling high-fidelity Gibbs state preparation for unseen Hamiltonian parameters. In quantum Boltzmann machine training, convergence accelerates by up to 30× over standard VarQITE, while initialization quality improves significantly. The framework exhibits strong scalability and robust generalization across diverse physical models.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Metareasoning and Metaheuristics
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Efficient preparation of quantum Gibbs states for parametrized Hamiltonians
• Generalizing Gibbs state preparation to unseen parameters via meta-learning
• Enhancing Quantum Boltzmann Machine training efficiency and accuracy

Innovation

• Meta-learning algorithms for quantum thermal state preparation
• Quantum-classical hybrid architecture for Gibbs states
• Warm start initializations for larger quantum systems