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:查找量子多体系统的地面状态是量子物理中的一个基本问题。 在这项工作中, 我们给出一种古典机器学习算法, 用于预测具有感应偏差编码几何位置的地面状态属性。 拟议的 ML 模型在只从 $\ mathcal{O} (\log(n) ) 中学习关于同一量子阶段其他汉密尔顿人的数据后, 可以有效地预测当地汉密尔顿人的地面状态属性为 $n- qubit 。 这比以前需要 $\ mathcal{O} (n ⁇ c) 数据的结果大有改进。 此外, 以 $\ mathcal{O} (n\ log n) 为Qubits 数量中的拟议 ML 模型的培训和预测时间为 $\ mathcal{O} (n\ log n) 。 在最多45 Qubits 物理系统上进行的数值实验证实了使用小型培训数据集预测地面状态属性的有利比例。