论文标题
带有噪音的古典阴影
Classical Shadows With Noise
论文作者
论文摘要
经典的阴影协议，最近由黄，Kueng和Preskill [Nat。物理。 16，1050（2020）]是一种量子古典方案，用于估计未知量子状态的性质。与完整的量子状态断层扫描不同，该协议可以在近期量子硬件上实施，并且需要很少的量子测量来以很高的成功概率进行许多预测。在本文中，我们研究噪声对经典阴影协议的影响。特别是，我们考虑了该方案中涉及的量子电路受到各种已知噪声通道的影响，并根据局部和全局噪声的阴影静音词来得出样本复杂性的分析上限。此外，通过修改无噪声协议的经典后处理步骤，我们定义了一个新的估计器，该估计量在存在噪声的情况下保持公正。作为应用，我们表明我们的结果可用于在去极化噪声和振幅阻尼的情况下证明严格的样品复杂性上限。
The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown quantum state. Unlike full quantum state tomography, the protocol can be implemented on near-term quantum hardware and requires few quantum measurements to make many predictions with a high success probability. In this paper, we study the effects of noise on the classical shadows protocol. In particular, we consider the scenario in which the quantum circuits involved in the protocol are subject to various known noise channels and derive an analytical upper bound for the sample complexity in terms of a shadow seminorm for both local and global noise. Additionally, by modifying the classical post-processing step of the noiseless protocol, we define a new estimator that remains unbiased in the presence of noise. As applications, we show that our results can be used to prove rigorous sample complexity upper bounds in the cases of depolarizing noise and amplitude damping.
