噪声缓解的随机测量与自校准阴影估计
Noise-mitigated randomized measurements and self-calibrating shadow estimation
AI总结：
针对随机测量中随机门噪声限制协议适用性的问题，提出误差缓解的随机测量方法，结合傅里叶变换框架关联随机基准测试与阴影估计，实现同次实验完成噪声缓解与鲁棒阴影估计，并提供严格性能保证与数值验证。
摘要：
随机测量作为估计量子系统特性的有力工具（例如在混合经典-量子计算表征中）正日益受到重视。在许多平台上，它们是原生可实现的测量方式，是阴影估计（shadow estimation）等主流方案的基础模块。然而在实际场景中，这些方案核心的随机门实现易受多种噪声和缺陷影响，严重限制了协议的适用性。为减轻这一缺陷的影响，本文提出了一种误差缓解的随机测量方法，由此得到了鲁棒的阴影估计流程。在实践层面，我们证明误差缓解和阴影估计可在同一次量子实验会话中完成，从而确保我们能够应对并缓解影响随机测量的噪声。在数学层面，我们提出了一种基于傅里叶变换的框架，将随机基准测试（randomized benchmarking）与阴影估计联系起来。我们证明了严格的性能保证，并通过全面的数值模拟验证了其有效性。从概念层面而言，我们证明，若使用得当，来自随机基准测试方案的易获取数据已能提供宝贵的诊断信息，用于揭示噪声动力学并辅助量子学习流程。
英文摘要：
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible measurements, serving as the building block of prominent schemes like shadow estimation. In the real world, however, the implementation of the random gates at the core of these schemes is susceptible to various sources of noise and imperfections, strongly limiting the applicability of protocols. To attenuate the impact of this shortcoming, in this work we introduce an error-mitigated method of randomized measurements, giving rise to a robust shadow estimation procedure. On the practical side, we show that error mitigation and shadow estimation can be carried out using the same session of quantum experiments, hence ensuring that we can address and mitigate the noise affecting the randomization measurements. Mathematically, we develop a picture derived from Fourier-transforms to connect randomized benchmarking and shadow estimation. We prove rigorous performance guarantees and show the functioning using comprehensive numerics. More conceptually, we demonstrate that, if properly used, easily accessible data from randomized benchmarking schemes already provide such valuable diagnostic information to inform about the noise dynamics and to assist in quantum learning procedures.
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