Quantum federated learning (QFL) enables collaborative training of a quantum machine learning (QML) model among multiple clients possessing quantum computing capabilities, without the need to share their respective local data. However, the limited availability of quantum computing resources poses a challenge for each client to acquire quantum computing capabilities. This raises a natural question: Can quantum computing capabilities be deployed on the server instead? In this paper, we propose a QFL framework specifically designed for classical clients, referred to as CC-QFL, in response to this question. In each iteration, the collaborative training of the QML model is assisted by the shadow tomography technique, eliminating the need for quantum computing capabilities of clients. Specifically, the server constructs a classical representation of the QML model and transmits it to the clients. The clients encode their local data onto observables and use this classical representation to calculate local gradients. These local gradients are then utilized to update the parameters of the QML model. We evaluate the effectiveness of our framework through extensive numerical simulations using handwritten digit images from the MNIST dataset. Our framework provides valuable insights into QFL, particularly in scenarios where quantum computing resources are scarce.

量子联邦学习（QFL）可以在拥有量子计算能力的多个客户端之间协作训练量子机器学习（QML）模型，而无需共享各自的本地数据。然而，量子计算资源的有限性给每个客户获取量子计算能力带来了挑战。这就提出了一个自然的问题：量子计算能力可以部署在服务器上吗？在本文中，我们针对这个问题提出了一个专门为经典客户设计的QFL框架，简称CC-QFL。在每次迭代中，QML模型的协同训练均由阴影层析技术辅助，无需客户的量子计算能力。具体来说，服务器构建 QML 模型的经典表示并将其传输到客户端。客户端将其本地数据编码到可观察量上，并使用这种经典表示来计算本地梯度。然后利用这些局部梯度来更新 QML 模型的参数。我们使用 MNIST 数据集中的手写数字图像进行广泛的数值模拟，评估我们框架的有效性。我们的框架为 QFL 提供了宝贵的见解，特别是在量子计算资源稀缺的情况下。