论文标题
从极少数测量值中预测量子系统的许多特性
Predicting Many Properties of a Quantum System from Very Few Measurements
论文作者
论文摘要
预测复杂的大规模量子系统的特性对于开发量子技术至关重要。我们提出了一种有效的方法，用于使用几乎没有状态的测量值来构建量子状态的经典描述。该描述称为经典影子，可用于预测许多不同的属性：订单$ \ log M $测量值足以准确预测国家的不同功能，具有很高的成功概率。测量的数量与系统大小无关，并使信息理论下限饱和。此外，在完成测量后可以选择要预测的目标属性。我们通过广泛的数值实验来支持我们的理论发现。我们应用经典的阴影来预测量子保真度，纠缠熵，两点相关函数，局部可观察物的期望值以及多体局部汉密尔顿人的能量差异。数值结果突出了相对于先前已知的方法的经典阴影的优势。
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order $\log M$ measurements suffice to accurately predict $M$ different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.
