论文标题
量子近似优化算法在非马克维亚量子系统中
Quantum Approximate Optimization Algorithm in Non-Markovian Quantum Systems
论文作者
论文摘要
尽管量子近似优化算法（QAOA）证明了其量子至上，但其在嘈杂的中间尺度量子（NISQ）设备上的性能会受到复杂的噪音的影响，例如量子色的噪声。为了评估QAOA在这些噪音下的性能，本文介绍了一个在非马克维亚量子系统上运行QAOA的框架，该系统由增强系统模型表示。在此模型中，携带量子色噪声的非马克维亚环境被建模为由量子白色噪声驱动的辅助系统，该系统直接耦合到相应的主体系统。即算法的计算单元。使用此模型，我们将数学形式地将QAOA作为对增强系统的分段哈密顿控制，在那里我们还优化了控制深度以适合当前量子设备的电路深度。为了有效地模拟非马克维亚量子系统中的QAOA，进一步提出了使用量子轨迹的增强算法。最后，我们表明可以将非马克维亚性用作量子资源来实现QAOA的相对良好性能，这是我们提出的探索率的特征。
Although quantum approximate optimization algorithm (QAOA) has demonstrated its quantum supremacy, its performance on Noisy Intermediate-Scale Quantum (NISQ) devices would be influenced by complicated noises, e.g., quantum colored noises. To evaluate the performance of QAOA under these noises, this paper presents a framework for running QAOA on non-Markovian quantum systems which are represented by an augmented system model. In this model, a non-Markovian environment carrying quantum colored noises is modelled as an ancillary system driven by quantum white noises which is directly coupled to the corresponding principal system; i.e., the computational unit for the algorithm. With this model, we mathematically formulate QAOA as piecewise Hamiltonian control of the augmented system, where we also optimize the control depth to fit into the circuit depth of current quantum devices. For efficient simulation of QAOA in non-Markovian quantum systems, a boosted algorithm using quantum trajectory is further presented. Finally, we show that non-Markovianity can be utilized as a quantum resource to achieve a relatively good performance of QAOA, which is characterized by our proposed exploration rate.
