We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an underlying probability distribution and extract samples as DQC expectation values. Using quantile mechanics we propagate the system in time, thereby allowing for time-series generation. We test the method by simulating the Ornstein-Uhlenbeck process and sampling at times different from the initial point, as required in financial analysis and dataset augmentation. Additionally, we analyse continuous quantum generative adversarial networks (qGANs), and show that they represent quantile functions with a modified (reordered) shape that impedes their efficient time-propagation. Our results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE-based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.
翻译:我们提出从随机差异方程式(SDEs)溶液中取样的量子算法。我们使用不同量子电路(DQCs),并配有潜伏变量的特征编码,代表基本概率分布的量子函数,提取样本作为DQC预期值。我们利用量子力学来及时传播系统,从而允许时间序列的生成。我们通过模拟Ornstein-Uhlenbeck过程,并在与初始点不同时段进行取样,如财务分析和数据元件增强所要求的那样,来测试该方法。此外,我们分析连续量子基因对抗网络(QGANs),并显示它们代表的量子功能,其形状经过修改(重新排序),阻碍其有效的时间调整。我们的结果揭示了量子量子力力力力学(QM)和qGANs(qGANs)之间在基于SDE的分布上的联系,并指出模型培训的差别限制的重要性,类似于物理知情神经网络最近的成功。