用量子蒙特卡洛模拟的自旋算符字符串做机器学习输入,可精准识别量子相变。
Learning phases with Quantum Monte Carlo simulation cell
- 将量子蒙特卡洛模拟结果转化为紧凑的自旋算符字符串作为输入
- 在相变识别和非局域可观测量预测上优于传统自旋构型
- 模型具备可解释性,能捕捉物理上有意义的特征
我们提出使用从随机级数展开量子蒙特卡洛(QMC)模拟中提取的“自旋算符字符串”(spin-opstring)作为机器学习(ML)输入数据。该表示法紧凑且内存高效,结合了初始态与编码虚时演化的算符串。通过监督学习,我们证明其在捕捉常规与拓扑相变、以及回归任务中预测非局域可观测量方面的有效性。此外,展示了该数据在迁移学习中的能力:在一种量子系统上训练的模型可成功预测另一系统;小尺寸系统训练的模型也能良好泛化至更大系统。重要的是,我们证明自旋算符字符串在准确预测量子相变方面显著优于传统自旋构型。最后,利用两种前沿可解释性技术——逐层相关传播(LRP)与SHapley加性解释(SHAP),表明模型学习并依赖于输入数据中的物理有意义特征。这些成果确立了自旋算符字符串作为量子多体物理中通用且可解释的机器学习输入格式。
原文摘要 · Abstract (English)
We propose the use of the ``spin-opstring", derived from Stochastic Series Expansion Quantum Monte Carlo (QMC) simulations as machine learning (ML) input data. It offers a compact, memory-efficient representation of QMC simulation cells, combining the initial state with an operator string that encodes the state's evolution through imaginary time. Using supervised ML, we demonstrate the input's effectiveness in capturing both conventional and topological phase transitions, and in a regression task to predict non-local observables. We also demonstrate the capability of spin-opstring data in transfer learning by training models on one quantum system and successfully predicting on another, as well as showing that models trained on smaller system sizes generalize well to larger ones. Importantly, we illustrate a clear advantage of spin-opstring over conventional spin configurations in the accurate prediction of a quantum phase transition. Finally, we show how the inherent structure of spin-opstring provides an elegant framework for the interpretability of ML predictions. Using two state-of-the-art interpretability techniques, Layer-wise Relevance Propagation and SHapley Additive exPlanations, we show that the ML models learn and rely on physically meaningful features from the input data. Together, these findings establish the spin-opstring as a broadly-applicable and interpretable input format for ML in quantum many-body physics.
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