AI 中文总结
针对量子计算最优控制问题，提出无超参数和梯度的PEPRino算法，利用响应理论框架，通过确定无限阶响应函数的控制格局并有效评估，应用于多量子比特系统实现QFT，相比CRAB算法在迭代步骤和计算时间上收敛更快。
AI 中文摘要
最优控制问题在众多科学学科中出现，但其优化算法常强烈依赖显著影响性能和收敛的超参数。对于量子算法的最优实现，高维控制格局和高保真操作需求进一步加剧了这些挑战。本文提出一种用于量子计算中最优控制问题的算法，能以无超参数和梯度的方式为多量子比特系统高效生成高保真控制协议。该方法即通过无限非线性阶响应函数投影的脉冲工程（PEPRino），利用响应理论框架在控制格局中找到高保真实现。通过确定无限阶响应函数的控制格局，并根据一阶和二阶响应函数进行重求和有效评估来实现。为演示该方法，将其应用于由两个和三个量子比特组成的量子系统以实现量子傅里叶变换（QFT）的最优实现。针对2量子比特场景，将该算法与利用Nelder-Mead方法的截断随机基（CRAB）算法进行基准测试。结果表明在迭代步骤和计算时间方面收敛更快，突出了该方法的优势。
英文摘要
Optimal control problems arise in a wide range of scientific disciplines, but the corresponding optimization algorithms often display a strong dependence on hyperparameters that significantly influence performance and convergence. For the optimal implementation of quantum algorithms, these challenges are further amplified by high-dimensional control landscapes and the need for high-fidelity operations. Here, we propose an algorithm for optimal control problems in quantum computing to efficiently generate high-fidelity control protocols for multi-qubit systems in a hyperparameter and gradient free manner. The method, referred to as Pulse Engineering via Projection of response functions at infinite nonlinear order (PEPRino), leverages the framework of response theory to navigate the control landscape to find high-fidelity implementations. This is achieved by determining the control landscape via response functions to infinite order, efficiently evaluated by resummation in terms of the first and second order response function. To demonstrate the approach, we apply it to quantum systems consisting of two and three qubits for the optimal implementation of the Quantum Fourier Transform (QFT). We benchmark the proposed algorithm against the Chopped Random Basis (CRAB) algorithm utilizing the Nelder-Mead method, focusing on the 2-qubit scenario. The results indicate faster convergence regarding iteration steps and computational time, highlighting the advantages of our approach.
