In the present study, we delineate a strategy focused on non-parametric quantum circuits for the generation of Gaussian random variables (GRVs). This quantum-centric approach serves as a substitute for conventional pseudorandom number generators (PRNGs), such as the \textbf{torch.rand} function in PyTorch. The principal theme of our research is the incorporation of Quantum Random Number Generators (QRNGs) into classical models of diffusion. Notably, our Quantum Gaussian Random Variable Generator fulfills dual roles, facilitating simulations in both Stable Diffusion (SD) and Brownian Motion (BM). This diverges markedly from prevailing methods that utilize parametric quantum circuits (PQCs), often in conjunction with variational quantum eigensolvers (VQEs). Although conventional techniques can accurately approximate ground states in complex systems or model elaborate probability distributions, they require a computationally demanding optimization process to tune parameters. Our non-parametric strategy obviates this necessity. To facilitate assimilating our methodology into existing computational frameworks, we put forward QonFusion, a Python library congruent with both PyTorch and PennyLane, functioning as a bridge between classical and quantum computational paradigms. We validate QonFusion through extensive statistical testing, including tests which confirm the statistical equivalence of the Gaussian samples from our quantum approach to classical counterparts within defined significance limits. QonFusion is available at \url{https://boltzmannentropy.github.io/qonfusion.github.io/} to reproduce all findings here.

本研究提出了一种基于非参数量子电路生成高斯随机变量的策略，该方法用于取代传统的伪随机数生成器，并将量子随机数生成器(QRNGs)纳入扩散的经典模型。通过非参数量子策略，我们成功实现了在稳定扩散和布朗运动中进行模拟，从而摆脱了传统方法所需的复杂优化过程。为了便于将我们的方法融入现有的计算框架，我们提出了QonFusion，这是一个与PyTorch和PennyLane兼容的Python库，作为经典和量子计算范式之间的桥梁。我们通过广泛的统计测试验证了QonFusion，包括确认量子方法生成的高斯样本与经典对应物在定义的显著性限度内的统计等价性。

QonFusion -- 高斯随机变量的量子方法: 稳定扩散和布朗运动的应用