标题： 经典与量子储备计算：在机器学习中的发展与应用 显示英文标题

标题： Classical and quantum reservoir computing: development and applications in machine learning

摘要： 储层计算是一种新颖的机器学习算法，它使用非线性动力系统，从数据中高效地学习复杂的时序模式。 本论文的目标是研究储层计算的原理，并开发最先进的变体，以解决机器学习中的各种应用。 研究表明，该算法在非常不同的领域中具有鲁棒性和适应性，包括农业时间序列预测以及量子系统的时序传播。 本论文的第一项贡献是开发了一种基于储层计算的方法，用于预测未来的农产品价格，这对于确保食品市场的可持续性至关重要。 论文的下一项贡献致力于求解复杂量子系统的薛定谔方程。 提出了一种新的储层计算框架，以高效地在时间上传播量子波函数，从而能够在特定能量范围内计算量子系统的全部本征态。 这种方法被用于研究量子化学和量子混沌领域的显著系统。 本论文的最后一项贡献集中在优化量子储层计算的算法设计。 结果表明，根据主要化准则，复杂度更高的量子电路家族在量子机器学习中表现出更优越的性能。 此外，评估了量子噪声对算法性能的影响，结果表明幅度阻尼噪声实际上可以提高量子储层计算的性能，而去极化噪声和相位阻尼噪声应优先进行校正。 此外，采用了最优的量子储层设计来构建一个混合量子-经典神经网络，以解决药物设计中的一个基本问题。 显示英文摘要

摘要： Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing and develop state-of-the-art variants capable of addressing diverse applications in machine learning. The research demonstrates the algorithm's robustness and adaptability across very different domains, including agricultural time series forecasting and the time propagation of quantum systems. The first contribution of this thesis consists in developing a reservoir computing-based methodology to predict future agricultural product prices, which is crucial for ensuring the sustainability of the food market. The next contribution of the thesis is devoted to solving the Schr\"odinger equation for complex quantum systems. A novel reservoir computing framework is proposed to efficiently propagate quantum wavefunctions in time, enabling the computation of all eigenstates of a quantum system within a specific energy range. This approach is used to study prominent systems in the field of quantum chemistry and quantum chaos. The last contribution of this thesis focuses on optimizing algorithm designs for quantum reservoir computing. The results demonstrate that families of quantum circuits with higher complexity, according to the majorization criterion, yield superior performance in quantum machine learning. Moreover, the impact of quantum noise on the algorithm performance is evaluated, revealing that the amplitude damping noise can actually be beneficial for the performance of quantum reservoir computing, while the depolarizing and phase damping noise should be prioritized for correction. Furthermore, the optimal design of quantum reservoirs is employed to construct a hybrid quantum-classical neural network that tackles a fundamental problem in drug design.