Quantum machine learning is often highlighted as one of the most promising uses for a quantum computer to solve practical problems. However, a major obstacle to the widespread use of quantum machine learning models in practice is that these models, even once trained, still require access to a quantum computer in order to be evaluated on new data. To solve this issue, we suggest that following the training phase of a quantum model, a quantum computer could be used to generate what we call a classical shadow of this model, i.e., a classically computable approximation of the learned function. While recent works already explore this idea and suggest approaches to construct such shadow models, they also raise the possibility that a completely classical model could be trained instead, thus circumventing the need for a quantum computer in the first place. In this work, we take a novel approach to define shadow models based on the frameworks of quantum linear models and classical shadow tomography. This approach allows us to show that there exist shadow models which can solve certain learning tasks that are intractable for fully classical models, based on widely-believed cryptography assumptions. We also discuss the (un)likeliness that all quantum models could be shadowfiable, based on common assumptions in complexity theory.

本文提出了一种基于量子线性模型和经典影子重构的方法来构建可在经典计算机上运行的量子机器学习模型，从而绕过访问量子计算机的需要，并对可实现经典阴影模型的学习任务及其复杂性进行了讨论。

量子机器学习的阴影