论文标题
蒙特卡洛集成的量子相对于尺寸的数量及其在融资中的应用
Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance
论文作者
论文摘要
使用量子计算机进行了广泛研究，包括用于混凝土问题的应用。众所周知，基于量子振幅估计（QAE）的量子算法可以计算一个积分，该积分与量子电路的数量较少的迭代调用，该量子电路的计算集成电器的迭代呼叫比经典方法称为Integrand subroutine。但是，有关集成电路中迭代操作的问题尚未如此多。也就是说，在高维积分中，使用许多随机数来计算积分，在某些情况下，重复进行类似的计算以获得集成的一个样本值。在本文中，我们指出，如果nested QAE的组合和使用伪数字（PRN）的组合，我们可以减少此类重复操作的数量，如果集成体对不同随机数的贡献具有可分离的形式。在本文中，作者最初在量子算法的上下文中提出的PRN的使用也是本文的关键因素，因为它可以平行地计算intapterand中的可分离项。此外，我们在金融，信用组合风险衡量方面选择了这种方法的一种用例，并估计复杂性在多大程度上降低。
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a smaller number of iterative calls of the quantum circuit which calculates the integrand, than classical methods call the integrand subroutine. However, the issues about the iterative operations in the integrand circuit have not been discussed so much. That is, in the high-dimensional integration, many random numbers are used for calculation of the integrand and in some cases similar calculations are repeated to obtain one sample value of the integrand. In this paper, we point out that we can reduce the number of such repeated operations by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers. The use of PRNs, which the authors originally proposed in the context of the quantum algorithm for Monte Carlo, is the key factor also in this paper, since it enables parallel computation of the separable terms in the integrand. Furthermore, we pick up one use case of this method in finance, the credit portfolio risk measurement, and estimate to what extent the complexity is reduced.
