论文标题
通过张量网络和正交函数扩展中提取用量子态振幅编码的函数
Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
论文作者
论文摘要
有一些量子算法用于查找满足一组条件的函数$ f $，例如求解部分微分方程，并且与现有的经典方法相比，这些算法达到了指数量子的加速，尤其是当变量的$ f $的数字$ d $ d $是较大时。但是，通常，这些算法输出了编码幅度$ f $的量子状态，并读出$ f $的值，因为来自这种状态的经典数据可能很耗时，以至于量子加速损坏。在这项研究中，我们为此功能读取任务提出了一种通用方法。基于张量网络和正交函数扩展的组合函数近似，我们提出了一个量子电路及其优化程序，以获得$ f $的近似函数，该函数具有相对于$ d $的多项式自由度，并且可以在经典计算机上有效地评估。我们还进行了数值实验，以近似融资动机的功能，以证明我们的方法有效。
There are quantum algorithms for finding a function $f$ satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the number $d$ of the variables of $f$ is large. In general, however, these algorithms output the quantum state which encodes $f$ in the amplitudes, and reading out the values of $f$ as 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 of $f$ that has a polynomial number of degrees of freedom with respect to $d$ and 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.
