Recent work has demonstrated the utility of introducing non-linearity through repeat-until-success (RUS) sub-routines into quantum circuits for generative modeling. As a follow-up to this work, we investigate two questions of relevance to the quantum algorithms and machine learning communities: Does introducing this form of non-linearity make the learning model classically simulatable due to the deferred measurement principle? And does introducing this form of non-linearity make the overall model's training more unstable? With respect to the first question, we demonstrate that the RUS sub-routines do not allow us to trivially map this quantum model to a classical one, whereas a model without RUS sub-circuits containing mid-circuit measurements could be mapped to a classical Bayesian network due to the deferred measurement principle of quantum mechanics. This strongly suggests that the proposed form of non-linearity makes the model classically in-efficient to simulate. In the pursuit of the second question, we train larger models than previously shown on three different probability distributions, one continuous and two discrete, and compare the training performance across multiple random trials. We see that while the model is able to perform exceptionally well in some trials, the variance across trials with certain datasets quantifies its relatively poor training stability.

翻译：近期研究表明，通过重复直到成功（RUS）子程序在量子电路中引入非线性，对生成式建模具有实用价值。作为该工作的后续研究，我们探讨了量子算法与机器学习领域相关的两个问题：这种非线性形式的引入是否因延迟测量原理导致学习模型具有经典可模拟性？以及这种非线性形式是否会使整体模型训练更加不稳定？针对第一个问题，我们证明RUS子程序无法使该量子模型被简单映射为经典模型——而根据量子力学延迟测量原理，不含RUS子电路但包含测量中间过程的模型可被映射为经典贝叶斯网络。这强烈表明所提出的非线性形式使得模型在经典计算中难以高效模拟。在探讨第二个问题时，我们训练了较以往研究更大的模型，针对三个不同概率分布（一个连续分布与两个离散分布），在多个随机试验中比较训练性能。结果表明：尽管模型在某些试验中表现极佳，但对于特定数据集，不同试验间的方差量化揭示了其相对较差的训练稳定性。