arXiv 2603.112072026-03-11quant-ph

通用主方程动力学的Kraus映射闭式解

Kraus map closed-form solution for general master equation dynamics

Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8)（于利希研究中心有限公司彼得·格林伯格研究所量子控制部门（PGI-8））

Shahrukh Chishti, Francisco Andrés Cárdenas-López, Felix Motzoi

备注：: 5 pages, 2 figures

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AI总结：

本文提出了一种通用主方程动力学的Kraus映射闭式解，适用于任意强驱动情况，通过黎曼和形式实现高精度数值模拟，为量子计算中的有效模型提供支持。

摘要：

量子通道的Kraus表示允许精确模拟量子处理器上复杂的动态，无论是在算法基准测试、预测纠错和缓解性能还是其他编译数字序列的众多应用中。然而，从基本原理出发获得连续量子主方程涉及各种近似，如与环境的弱耦合。进一步，将这些方程转换为Kraus算子通常无法用闭式表达，因为该问题的复杂交换子结构。在我们的工作中，我们通过提供一个任意强驱动的一般闭式公式来弥合这一差距，同时保持在耗散子中线性。Kraus解以黎曼和形式表达，其中更高阶项可以快速收敛到高精度，我们通过数值方法演示了这一点。这种公式对于量子计算和基于门的模型具有高度相关性，因为在大旋转门角下有效模型备受需求，即使在底层非平凡噪声机制的影响下。

英文摘要：

The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation, or in the myriad other uses of compiled digital sequences. Nonetheless, starting from first principles to obtain continuous quantum master equations involves various approximations such as weak coupling to the environment. Further, converting these equations to Kraus operators cannot generally be obtained in closed-form due to the complicated commutator structure of the problem. In our work, we bridge this gap by providing a general closed form formulation for arbitrarily strong driving while remaining linear in the dissipator. The Kraus solution is expressed as a Riemann sum where higher terms can converge quickly to high precision, which we demonstrate numerically. Such a formulation is highly relevant to quantum computing and gate-based models, where effective models are highly sought for large rotation gate angles, even under the influence of underlying non-trivial noise mechanisms.

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