论文标题
量子量子分类器和支持向量机的量子内核的普遍表现
Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines
论文作者
论文摘要
机器学习被认为是量子计算最有前途的应用之一。因此，寻找机器学习模型的量子类似物的量子优势是一个关键的研究目标。在这里，我们表明，具有量子内核的变量量子分类器和支持向量机可以根据$ k $ - - 相关问题解决分类问题，该问题已知是PromiseBQP complete。由于PromistBQP复杂性类别包括所有有界的量子量子多项式时间（BQP）决策问题，因此我们的结果暗示存在特征图和量子内核，这些量子内核使变量量子量子分类器和量子内核支持向量机有效地解决了任何BQP问题。因此，这项工作意味着他们的特征图和量子内核可以设计为具有在多项式时间内无法经典求解的任何分类问题具有量子优势，而与量子计算机相反。
Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer.
