论文标题
部分可观测时空混沌系统的无模型预测
Quantum algorithm for neural network enhanced multi-class parallel classification
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the basis of the quantum state in quantum circuit composed by \emph{sample register} and \emph{label register}, and the parameters of quantum gates are optimized by a hybrid quantum-classical method, which is composed of a trainable quantum circuit and a gradient-based classical optimizer. After several quantum-to-class repetitions, the quantum state is optimal that the state in \emph{sample register} is the same as that in \emph{label register}. %A structure of loading data many times is performed as a quantum version of neural network to improve the expression ability of quantum circuit. For a classification task of $L$-class, the analysis shows that the space and time complexity of the quantum circuit are $O(L*logL)$ and $O(logL)$, respectively. The numerical simulation results of 2-class task and 5-class task show that the proposed algorithm has a higher classification accuracy, faster convergence and higher expression ability. The classification accuracy and the speed of converging can also be improved by increasing the number times of applying multi-qubit controlled operators on the quantum circuit, especially for multiple classes classification.
