离散随机过程的量子增强分析
Quantum-enhanced analysis of discrete stochastic processes
摘要：
离散随机过程（DSP）是概率系统动力学建模的工具，在科学和工程中有广泛的应用。DSP通常通过蒙特卡罗方法进行分析，因为实现的数量随着时间步长的数量呈指数增长，并且通常需要重要性采样来减少方差。我们提出了一个量子算法来计算DSP的特征函数，它完全定义了它的概率分布，使用的量子线路元素的数量只与时间步长的数量线性增长。量子算法考虑了所有的随机轨迹，从而消除了重要性采样的需要。该算法可以进一步配备量子幅度估计算法，以提供二次采样加速。这两种策略都提高了传统能力之外的方差。量子方法可以与傅立叶近似相结合，以估计随机变量的任何可积函数的期望值。在金融和相关随机游动的应用，以证明我们的结果的有用性。使用IBM量子云平台进行原理验证实验。
英文摘要：
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP, which completely defines its probability distribution, using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm takes all stochastic trajectories into account and hence eliminates the need of importance sampling. The algorithm can be further furnished with the quantum amplitude estimation algorithm to provide quadratic speed-up in sampling. Both of these strategies improve variance beyond classical capabilities. The quantum method can be combined with Fourier approximation to estimate an expectation value of any integrable function of the random variable. Applications in finance and correlated random walks are presented to exemplify the usefulness of our results. Proof-of-principle experiments are performed using the IBM quantum cloud platform.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
