Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
复制标题
DOI：
10.1007/s11128-023-03937-y
复制
发表时间：
2022-08
影响因子：
2.5
通讯作者：
Koichi Miyamoto;H. Ueda
中科院分区：
文献类型：
--
作者：
Koichi Miyamoto;H. Ueda
有一些量子算法可以找到满足一组条件的函数f，例如解偏微分方程，与现有的经典方法相比，这些算法实现了指数量子加速，特别是当f的变量数量很大时。然而，一般来说，这些算法输出的量子态编码的振幅，和阅读的值从这样一个状态的经典数据可以是如此耗时的量子加速被破坏。在这项研究中，我们提出了一个通用的方法，这个功能读出任务。基于张量网络和正交函数展开相结合的函数逼近方法，我们提出了一种量子电路及其优化方法，以获得一个具有多项式自由度的近似函数，该函数在经典计算机上是有效的。我们还进行了一个数值实验，以近似金融动机的功能，以证明我们的方法的作品。
There are quantum algorithms for finding a functionfsatisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the numberdof the variables offis large. In general, however, these algorithms output the quantum state which encodesfin the amplitudes, and reading out the values offas classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this study, we propose a general method for this function readout task. Based on the function approximation by a combination of tensor network and orthogonal function expansion, we present a quantum circuit and its optimization procedure to obtain an approximating function offthat has a polynomial number of degrees of freedom with respect todand is efficiently evaluable on a classical computer. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.