Hamilton-Zero：适用于任意二次量子比特哈密顿量基态的神经张量网络基础模型
Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians
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中文总结 AI 辅助
该研究提出Hamilton-Zero基础模型，将二次量子比特哈密顿量基态学习转化为流形变分优化，经预训练、微调后可在8100量子比特系统上评估，突破经典模拟局限，实现量子基态的高效计算。
中文摘要 AI 辅助
实用量子优势的核心承诺之一是计算超出经典模拟方法能力范围的哈密顿系统基态。本文展示，通过一个具有约0.5B变分参数的基础模型，该问题可在任意通用哈密顿量集合上实现摊销，该模型采用大语言模型和深度强化学习的现代技术训练。为此，我们将自旋-1/2量子基态学习公式化为对SU(2)^N上中心奇标量函数的流形变分优化，这将显式希尔伯特空间矢量振幅替换为流形函数，哈密顿量通过李导数作用于这些流形函数，由自定义自动微分原语计算。我们利用彼得-外尔定理证明，该流形上的变分原理保持自旋-1/2扇区基态的上界；随后，我们在包含数十万个不同哈密顿系统的数据集上预训练该基础模型，这些系统在连接拓扑、系统规模、相互作用类型及强度上存在差异，整合了一个世纪的多体研究成果。我们采用新型SU(2)副本交换朗之万采样器和分片自然梯度优化，通过对克罗内克分解近似曲率（KFAC）优化器的扩展，在多达64量子比特的系统规模上训练模型。在保留的泛化数据集上，我们对模型进行多达1024量子比特系统规模的微调，并在多达8100量子比特的系统上进行评估。
英文摘要
A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods. Here we demonstrate that this problem can be effectively amortized across an arbitrary and universal set of Hamiltonians by a foundation model with $\sim0.5$B variational parameters, trained with contemporary techniques from large language models and deep reinforcement learning. To do this, we formulate $\text{spin-}1/2$ quantum ground-state learning as manifold variational optimisation over centrally odd scalar functions on $\mathrm{SU}(2)^N$. This replaces explicit Hilbert-space vector amplitudes with manifold functions on which the Hamiltonian acts through Lie derivatives, evaluated by custom automatic differentiation primitives. We prove that the resulting variational principle on this manifold preserves the $\text{spin-}1/2$ sector's ground-state upper bound using the Peter-Weyl theorem and justify the choice of such a representation with a no-go theorem for pure state foundation NQS. We then pre-train our foundation model on a dataset of hundreds of thousands of different Hamiltonian systems, varying the connection topology, system size, interaction types and strengths, bringing together a century of many-body literature. Using a novel $\mathrm{SU}(2)$ replica-exchange Langevin sampler and sharded natural-gradient optimisation, we train our model with our own extension of the Kronecker-Factored Approximate Curvature (KFAC) optimiser on system sizes up to 64 qubits. On a held-out generalisation dataset, we fine-tune our model on system sizes of up to 1024 qubits, and evaluate on systems up to 8100 qubits.
发表机构
- Simulacra Research Inc.（模拟研究公司）
- ICFO – Institut de Ciències Fotòniques（ICFO – 光子科学研究所）
- The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究院）
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