神经网络增强多类并行分类的量子算法
Quantum algorithm for neural network enhanced multi-class parallel classification
摘要：
利用量子叠加的性质，提出了一种有效的多类分类算法。该算法将训练数据加载到参数化算子中，并将其应用于由\emph{sample register}和\emph{label register}组成的量子线路中的量子态基，同时采用量子-经典混合方法优化量子门的参数，其由可训练的量子线路和基于梯度的经典优化器组成。在几次量子到类的重复之后，量子态是最佳的，即\emph{sample register}中的状态与\emph{label register}中的状态相同。提出了一种多次加载数据的结构作为量子形式的神经网络，以提高量子线路的表达能力。对于一个$L$类的分类任务，分析表明量子线路的空间复杂度和时间复杂度分别为$O(L*logL)$和$O(logL)$。对2类任务和5类任务的数值仿真结果表明，该算法具有更高的分类精度、更快的收敛速度和更强的表达能力。通过增加多量子比特控制算子在量子线路上的应用次数，可以提高分类精度和收敛速度，尤其是对于多类分类。
英文摘要：
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.
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