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.

翻译：量子机器学习常被强调为量子计算机解决实际问题最有前途的应用之一。然而，量子机器学习模型在实际中广泛使用的一个主要障碍是，即使这些模型经过训练，在评估新数据时仍需要访问量子计算机。为了解决这一问题，我们建议在量子模型的训练阶段之后，利用量子计算机生成所谓的该模型的经典阴影，即学习函数的经典可计算近似。尽管近期已有研究探索了这一想法并提出了构建此类阴影模型的方法，但这些研究也提出了另一种可能性：或许可以直接训练一个完全经典的模型，从而从一开始就规避对量子计算机的需求。在本工作中，我们基于量子线性模型和经典阴影层析成像框架，提出了一种定义阴影模型的新方法。这一方法使我们能够证明，基于广泛接受的密码学假设，存在某些阴影模型可以解决完全经典模型难以处理的特定学习任务。我们还基于复杂性理论中的常见假设，讨论了所有量子模型均可被阴影化的可能性（或不可能性）。