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.

翻译：本研究阐述了一种基于非参数量子电路生成高斯随机变量的策略。这种以量子为核心的方法可作为传统伪随机数生成器的替代方案，例如PyTorch中的**torch.rand**函数。我们研究的主旨是将量子随机数生成器整合到经典扩散模型中。值得注意的是，我们的量子高斯随机变量生成器具有双重功能，能够同时支持稳定扩散和布朗运动的模拟。这显著区别于当前主流方法——这些方法常采用参数化量子电路并结合变分量子本征求解器。尽管传统技术能精确逼近复杂系统中的基态或建模精细的概率分布，但需要耗费大量算力的参数优化过程。我们的非参数策略则免除了这一需求。为便于将该方法融入现有计算框架，我们提出了QonFusion——一个兼容PyTorch与PennyLane的Python库，作为经典与量子计算范式之间的桥梁。我们通过广泛的统计检验验证了QonFusion，包括在指定显著性水平下确认量子方法生成的高斯样本与经典样本具有统计等价性的测试。QonFusion开源代码及所有可重复实验数据参见：\url{https://boltzmannentropy.github.io/qonfusion.github.io/}。