论文标题
用于估计特征值的量子算法
Quantum Algorithm For Estimating Eigenvalue
论文作者
论文摘要
大多数数值科学计算在很大程度上都依赖于处理和操纵矩阵，例如求解线性方程，查找特征值和特征向量等等。已经开发了许多量子算法来推进这些计算任务，在某些情况下，例如求解线性方程式，可以证明可以产生指数加速。在这里，采用HHL算法中的技术和经典功率方法的思想，我们提供了一种简单的量子算法，用于估算给定的Hermitian矩阵的最大特征值。与HHL算法一样，与解决相同问题的经典算法相比，我们的量子程序也可以产生指数加速。我们还讨论了我们的量子算法的一些可能的扩展和应用，例如混合量子古典的兰氏算法的版本。
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance these computational tasks, and in some cases, such as solving linear equations, can be shown to yield exponential speedup. Here, employing the techniques in the HHL algorithm and the ideas of the classical power method, we provide a simple quantum algorithm for estimating the largest eigenvalue in magnitude of a given Hermitian matrix. As in the case of the HHL algorithm, our quantum procedure can also yield exponential speedup compared to classical algorithms that solve the same problem. We also discuss a few possible extensions and applications of our quantum algorithm, such as a version of a hybrid quantum-classical Lanczos algorithm.
