Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.

翻译：许多推理场景依赖于从已知数据中提取相关信息以进行未来预测。当底层随机过程满足特定假设时，其经典与量子模拟器之间存在直接映射关系，后者在渐近意义上使用更少的内存。本文聚焦于研究当这些假设不成立且模型必然存在不完美精度时，此类量子优势是否依然存在。通过考察精度与内存需求之间的权衡，我们证明量子模型能够以更少的内存达到相同精度，或在相同内存条件下实现更高精度。最后，我们讨论了这一结果对学习任务的启示。