Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not possible to fully describe noisy gates locally in time if noise is correlated on times longer than their duration. To address this issue, we develop a method based on the filter function formalism to perturbatively compute quantum processes in the presence of correlated classical noise. We derive a composition rule for the filter function of a sequence of gates in terms of those of the individual gates. The joint filter function allows us to efficiently compute the quantum process of the whole sequence. Moreover, we show that correlation terms arise which capture the effects of the concatenation and, thus, yield insight into the effect of noise correlations on gate sequences. Our generalization of the filter function formalism enables both qualitative and quantitative studies of algorithms and state-of-the-art tools widely used for the experimental verification of gate fidelities like randomized benchmarking, even in the presence of noise correlations.

中文翻译：

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相关噪声下量子过程的滤波函数

许多量子位实现受到基于马尔可夫近似的标准理论工具未捕获的相关噪声的影响。虽然独立门操作是量子计算的一个关键概念，但如果噪声的相关时间长于其持续时间，则实际上不可能在本地及时完整地描述噪声门。为了解决这个问题，我们开发了一种基于滤波器函数形式主义的方法，以在存在相关经典噪声的情况下微扰计算量子过程。我们根据各个门的过滤功能推导出一系列门的过滤函数的组合规则。联合滤波器函数使我们能够有效地计算整个序列的量子过程。此外，我们展示了相关项的出现，它们捕捉了串联的影响，因此，深入了解噪声相关性对门序列的影响。我们对滤波器函数形式主义的推广能够对算法和最先进的工具进行定性和定量研究，这些工具广泛用于门保真度的实验验证，例如随机基准测试，即使在存在噪声相关性的情况下也是如此。