Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log(n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n \log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

翻译：寻找量子多体系统的基态是量子物理学中的一个基本问题。本文提出了一种具有编码几何局域性的归纳偏置的经典机器学习（ML）算法，用于预测基态性质。该ML模型在仅从同一量子物相中其他哈密顿量的$\mathcal{O}(\log(n))$数据中学习后，便能高效预测$n$量子比特带隙局域哈密顿量的基态性质。这显著优于此前需要$\mathcal{O}(n^c)$（其中$c$为大常数）数据量的方法。此外，该ML模型的训练与预测时间随量子比特数$n$呈$\mathcal{O}(n \log n)$缩放。在包含多达45个量子比特的物理系统上的数值实验证实，使用少量训练数据集预测基态性质具有优势缩放性能。