Quantum GAN with Distribution Initialization for Financial Option Pricing

Abstract

Quantum computers are gaining attention for their ability to solve certain problems faster than classical computers, and one area where they are considered useful is financial engineering, which heavily employs the Monte Carlo method. A previous study has shown that qGAN, a quantum circuit version of GAN, can generate the probability distribution necessary for the Monte Carlo method in shallow quantum circuits. However, a previous study has also suggested that the convergence speed and accuracy of the generated distribution can vary greatly depending on the initial distribution of the generator of qGAN. In particular, the effectiveness of using a normal distribution as the initial distribution has been claimed, but it requires a deep quantum circuit, which may lose the advantage of qGAN. Therefore, in this study, we propose a novel method for generating an initial distribution that improves the efficiency of qGAN learning. Our method uses the classical process of "label replacement" to generate various probability distributions in shallow quantum circuits similar to the uniform distribution. We demonstrate that our proposed method can generate the log-normal distribution, which is important in financial engineering, more efficiently than existing methods.