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arXiv 2602.08464quant-ph
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由泡利扭曲引起的非马尔可夫性

Non-Markovianity induced by Pauli-twirling

University of Konstanz（康斯坦茨大学）；Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen University（亚琛工业大学）

Joris Kattemölle, Balázs Gulácsi, Guido Burkard

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9 pages, 2 figures
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AI总结：

本研究指出，泡利扭曲可能导致非马尔可夫性，需使用负泡利-林布兰德参数以正确描述实验噪声。

摘要：

噪声是有效量子信息处理的主要障碍。最近的实验进展使人们能够通过泡利扭曲来定制噪声特性，将任意噪声通道转换为泡利通道。这为容错量子计算的理论描述奠定了基础，并成为噪声特性和错误缓解的重要工具。泡利-林布兰德通道已被引入，以准确参数化量子寄存器中的准局部泡利错误，排除了依赖于底层噪声过程马尔可夫性的负泡利-林布兰德参数。我们指出，当将通道参数化为具有非负参数的泡利-林布兰德通道时需谨慎。为此，我们研究了泡利扭曲对马尔可夫性的影响。我们使用通道的马尔可夫性（而不是整个半群）的概念，并证明一般泡利通道是非马尔可夫性的当且仅当至少有一个泡利-林布兰德参数为负。利用这一点，我们证明马尔可夫量子通道在泡利扭曲后往往变为非马尔可夫性。由泡利扭曲引起的非马尔可夫性需要使用负泡利-林布兰德参数来正确描述实验中实际的噪声。一个重要例子是标准马尔可夫噪声下√X门的实现。因此，我们的结果对依赖于准确噪声特性的量子错误缓解协议有直接影响。

英文摘要：

Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the $\sqrt{X}$-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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