用少量量子资源实现原子阵列相变的高精度分类
Quantum Phase Classification of Rydberg Atom Systems Using Resource-Efficient Variational Quantum Circuits and Classical Shadows
- 结合经典阴影与极简量子电路，通过角度编码提取特征
- 51原子系统下测试准确率100%，仅需2参数7层电路
- 适合想在小规模量子设备上做凝聚态物理研究的人
里德伯原子阵列中的量子相变为研究多体物理提供了重要机遇，但缺乏显式序参量时区分不同有序相仍具挑战。本文提出一种资源高效量子机器学习方法，结合经典阴影断层成像与变分量子电路（VQC），对Z2和Z3有序相进行二元分类。该流程对每条51原子链态执行500次随机测量，重构阴影算符，经主成分分析（PCA）降维至514维特征，再通过角度编码映射至2量子比特参数化电路。电路采用RY-RZ编码、全连接CZ门实现强纠缠，使用最小2参数波函数，深度仅为7。训练采用同时扰动随机近似（SPSA）与铰链损失，120次迭代即收敛。模型在测试集上达到100%准确率，精确率、召回率与F1分数均为完美值，证明极小量子资源即可实现高精度相分类。本工作为近中期量子设备上的量子增强凝聚态物理研究开辟路径。
原文摘要 · Abstract (English)
Quantum phase transitions in Rydberg atom arrays present significant opportunities for studying many-body physics, yet distinguishing between different ordered phases without explicit order parameters remains challenging. We present a resource-efficient quantum machine learning approach combining classical shadow tomography with variational quantum circuits (VQCs) for binary phase classification of Z2 and Z3 ordered phases. Our pipeline processes 500 randomized measurements per 51-atom chain state, reconstructs shadow operators, performs PCA dimensionality reduction (514 features), and encodes features using angle embedding onto a 2-qubit parameterized circuit. The circuit employs RY-RZ angle encoding, strong entanglement via all-to-all CZ gates, and a minimal 2-parameter ansatz achieving depth 7. Training via simultaneous perturbation stochastic approximation (SPSA) with hinge loss converged in 120 iterations. The model achieved 100% test accuracy with perfect precision, recall, and F1 scores, demonstrating that minimal quantum resources suffice for high-accuracy phase classification. This work establishes pathways for quantum-enhanced condensed matter physics on near-term quantum devices.
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