Quantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using quantum generative models with explicit losses such as the KL divergence leads to a new flavour of barren plateaus. In contrast, the implicit Maximum Mean Discrepancy loss can be viewed as the expectation value of an observable that is either low-bodied and provably trainable, or global and untrainable depending on the choice of kernel. In parallel, we find that solely low-bodied implicit losses cannot in general distinguish high-order correlations in the target data, while some quantum loss estimation strategies can. We validate our findings by comparing different loss functions for modelling data from High-Energy-Physics.

翻译：量子生成模型提供了本质上高效的采样策略，因此显示出利用量子硬件实现优势的潜力。在这项工作中，我们研究了由贫瘠高原和指数损失集中引起的量子生成模型可训练性障碍。我们探讨了显式与隐式模型及损失函数之间的相互作用，并证明使用具有显式损失（如KL散度）的量子生成模型会导致一种新形式的贫瘠高原。相比之下，隐式最大均值差异损失可被视为一个可观测量期望值，该可观测量根据核函数的选择，要么是低体的且可证明可训练的，要么是全局的且不可训练的。同时，我们发现仅凭低体隐式损失通常无法区分目标数据中的高阶相关性，而某些量子损失估计策略可以做到这一点。我们通过比较高能物理数据建模中的不同损失函数，验证了我们的发现。