标题： QUACK：量子对齐质心核 显示英文标题

标题： QUACK: Quantum Aligned Centroid Kernel

摘要： 量子计算（QC）似乎在机器学习（ML）中显示出应用潜力。 特别是量子核方法（QKM）在监督式ML任务中表现出有前景的特性。 然而，核方法的一个主要缺点是其与训练样本数量呈不利的二次增长关系。 结合目前可用的量子硬件（NISQ设备）所施加的限制，包括低量子比特相干时间、少量量子比特和高错误率，目前在工业相关规模上使用QC进行ML是不可能的。 作为改善QKM潜在应用的一个小步骤，我们引入了QUACK，这是一种量子核算法，其时间复杂度在训练过程中与样本数量呈线性关系，并且在推理阶段独立于训练样本数量。 在训练过程中，仅计算样本和类别中心的核条目，即 核的最大形状为n个样本和c个类别的(n, c)。 在训练过程中，量子核的参数和质心的位置是迭代优化的。 在推理阶段，对于每个新样本，电路仅针对每个质心进行评估，即 c次。 我们证明，尽管如此，QUACK算法仍然能提供令人满意的结果，并且在训练期间能够达到与经典核方法相似的水平。 此外，我们的（模拟）算法能够在没有任何降维的情况下处理高维数据集，如具有784个特征的MNIST。 显示英文摘要

摘要： Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods is their unfavorable quadratic scaling with the number of training samples. Together with the limits imposed by currently available quantum hardware (NISQ devices) with their low qubit coherence times, small number of qubits, and high error rates, the use of QC in ML at an industrially relevant scale is currently impossible. As a small step in improving the potential applications of QKMs, we introduce QUACK, a quantum kernel algorithm whose time complexity scales linear with the number of samples during training, and independent of the number of training samples in the inference stage. In the training process, only the kernel entries for the samples and the centers of the classes are calculated, i.e. the maximum shape of the kernel for n samples and c classes is (n, c). During training, the parameters of the quantum kernel and the positions of the centroids are optimized iteratively. In the inference stage, for every new sample the circuit is only evaluated for every centroid, i.e. c times. We show that the QUACK algorithm nevertheless provides satisfactory results and can perform at a similar level as classical kernel methods with quadratic scaling during training. In addition, our (simulated) algorithm is able to handle high-dimensional datasets such as MNIST with 784 features without any dimensionality reduction.