Federated Learning with Exponential Compression through Schmidt-Decomposition-Guided Quantum Circuits

A fundamental challenge in federated learning is communication overhead, where clients and servers exchange millions of model parameters or their gradients. In this work, we introduce a novel framework that leverages client-side quantum processors to achieve exponential communication compression while maintaining model accuracy. At each client, we employ a personalized quantum circuit whose architecture is directly optimized using the Schmidt decomposition of the client's local data spectrum. This data-aware design enables an exponential reduction in dimensionality, compressing $2^n$-dimensional data vectors into $n$-dimensional classical feature vectors ($2^n \!\to\! n$) for transmission. The server then trains a classical model on these aggregated, compressed features to perform the learning task. The approach provides a principled method for low-rank approximation and ensures a dramatic reduction in communication costs. We demonstrate experimental results on benchmark datasets including Iris, Digits, and CIFAR10. The results show that the framework maintains competitive accuracy while achieving up to 102.4× compression, establishing a practical pathway for communication bandwidth-constrained applications.