We introduce variational hybrid classical-quantum algorithms to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our methods are based on a direct representation of density matrices and quantum observables as quantum superstates. We design and optimize low-depth variational quantum circuits that efficiently capture the unitary and non-unitary dynamics of the solutions. We benchmark and test the algorithms on different models and system sizes, showing their potential for utility with near-future hardware.

中文翻译：

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用于模拟 Lindblad 动力学的变分量子算法

我们引入变分混合经典量子算法来模拟时间演化马尔可夫开放量子系统和量子可观测量的 Lindblad 主方程及其伴随方程。我们的方法基于密度矩阵和量子可观测量作为量子超状态的直接表示。我们设计和优化低深度变分量子电路，有效捕获解决方案的单一和非单一动力学。我们在不同模型和系统规模上对算法进行基准测试和测试，展示它们在近期硬件中的实用潜力。