论文标题
量子判别规范相关分析
Quantum discriminative canonical correlation analysis
论文作者
论文摘要
判别规范相关分析（DCCA）是两组多元数据的强大监督特征提取技术，该技术在模式识别中具有广泛的应用。 DCCA由两个部分组成：（i）均值中心，从样本中减去样本平均值； （ii）解决广义特征值问题。当处理大量高维样品时，DCCA的成本很昂贵。为了解决这个问题，我们在这里提出了一种量子DCCA算法。具体而言，我们设计了一种有效的方法来计算所有样品的平均值，然后使用块 - 哈米尔顿模拟和量子相估计来解决广义特征值问题。我们的算法在其经典对应物的某些条件下，在样品的维度上实现了多项式加速。
Discriminative Canonical Correlation Analysis (DCCA) is a powerful supervised feature extraction technique for two sets of multivariate data, which has wide applications in pattern recognition. DCCA consists of two parts: (i) mean-centering that subtracts the sample mean from the sample; (ii) solving the generalized eigenvalue problem. The cost of DCCA is expensive when dealing with a large number of high-dimensional samples. To solve this problem, here we propose a quantum DCCA algorithm. Specifically, we devise an efficient method to compute the mean of all samples, then use block-Hamiltonian simulation and quantum phase estimation to solve the generalized eigenvalue problem. Our algorithm achieves a polynomial speedup in the dimension of samples under certain conditions over its classical counterpart.
