用少量测量识别未知量子相，结合经典与量子技术实现高效分类。
Learning to Classify Quantum Phases of Matter with a Few Measurements
- 基于已有知识构造可观测量，指导新相位分类
- 某些情况下仅需多项式量级测量即可验证新基态
- 适合量子模拟器中受限测量场景的相分类任务
我们研究零温下量子物相的识别问题，当相图部分未知时，采用监督学习方法，利用已有知识构建可观测量，以对未知区域的相进行分类。结合张量网络、核方法、泛化界、量子算法和阴影估计算法等经典与量子技术，我们证明在某些情况下，新基态的认证仅需多项式数量的测量。该方法的重要应用是量子模拟器（如冷原子实验）中物相的分类，这些系统能高效制备复杂多体系统的基态，并施加简单测量（如单量子比特测量），但无法实现通用门集。
原文摘要 · Abstract (English)
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g., cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g., single qubit measurements, but unable to perform a universal set of gates.
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