Federated learning has emerged as a viable distributed solution to train machine learning models without the actual need to share data with the central aggregator. However, standard neural network-based federated learning models have been shown to be susceptible to data leakage from the gradients shared with the server. In this work, we introduce federated learning with variational quantum circuit model built using expressive encoding maps coupled with overparameterized ans\"atze. We show that expressive maps lead to inherent privacy against gradient inversion attacks, while overparameterization ensures model trainability. Our privacy framework centers on the complexity of solving the system of high-degree multivariate Chebyshev polynomials generated by the gradients of quantum circuit. We present compelling arguments highlighting the inherent difficulty in solving these equations, both in exact and approximate scenarios. Additionally, we delve into machine learning-based attack strategies and establish a direct connection between overparameterization in the original federated learning model and underparameterization in the attack model. Furthermore, we provide numerical scaling arguments showcasing that underparameterization of the expressive map in the attack model leads to the loss landscape being swamped with exponentially many spurious local minima points, thus making it extremely hard to realize a successful attack. This provides a strong claim, for the first time, that the nature of quantum machine learning models inherently helps prevent data leakage in federated learning.

翻译：联邦学习已成为一种可行的分布式解决方案，可在无需与中央聚合器共享数据的条件下训练机器学习模型。然而，基于标准神经网络的联邦学习模型已被证明易受梯度泄露攻击，攻击者可通过共享给服务器的梯度窃取数据。本研究提出一种基于变分量子电路模型的联邦学习方法，该模型采用富有表现力的编码映射与过参数化拟设。研究表明，富有表现力的映射能够针对梯度反演攻击提供内在隐私保护，而过参数化则确保模型的可训练性。我们的隐私框架核心在于求解由量子电路梯度生成的高阶多元切比雪夫多项式系统的复杂度。我们从精确解与近似解两个角度提出有力论据，论证这些方程固有的求解困难性。此外，我们深入探讨基于机器学习的攻击策略，并在原始联邦学习模型的过参数化与攻击模型的欠参数化之间建立直接关联。进一步地，我们通过数值标度论证表明，攻击模型中富有表现力映射的欠参数化会导致损失景观被指数级数量的伪局部极小点淹没，从而显著增加成功攻击的难度。这首次有力证明，量子机器学习模型的内在特性有助于从根本上防止联邦学习中的数据泄露。