用集合变压器提升量子态性质估计精度，显著降低误差。
Scalable bayesian shadow tomography for quantum property estimation with set transformers
- 结合经典阴影与集合变压器，直接预测量子性质
- 在少量样本下误差降低超99%，优于传统方法
- 适用于大规模量子系统，计算量随系统规模多项式增长
本文提出一种可扩展的贝叶斯机器学习框架，从测量数据中估算未知量子态的标量性质，无需完整密度矩阵重建。首次将经典阴影协议与置换不变的集合变压器架构结合，能够预测并校正现有估计器的偏差，逼近真实的贝叶斯后验均值。测量结果被编码为固定维度特征向量，网络输出对基线估计器的残差修正。通过输入规模与系统大小及测量次数呈多项式依赖，确保了对大尺度量子系统的可扩展性。在格林伯格-霍恩-蔡尔兹态保真度与二阶Rényi熵估计任务中（使用随机泡利和随机克莱夫顿测量），该贝叶斯估计器始终低于经典阴影的均方误差，在少样本情况下降幅超过99%。
原文摘要 · Abstract (English)
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the classical shadows protocol with a permutation-invariant set transformer architecture, enabling the approach to predict and correct bias in existing estimators to approximate the true Bayesian posterior mean. Measurement outcomes are encoded as fixed-dimensional feature vectors, and the network outputs a residual correction to a baseline estimator. Scalability to large quantum systems is ensured by the polynomial dependence of input size on system size and number of measurements. On Greenberger-Horne-Zeilinger state fidelity and second-order Rényi entropy estimation tasks -- using random Pauli and random Clifford measurements -- this Bayesian estimator always achieves lower mean squared error than classical shadows alone, with more than a 99\% reduction in the few copy regime.
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