arXiv Machine Learning By Marcel Mordarski, Nathan Mani, Arshad Patel, William Knottenbelt, Roberto Bondesan

Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks

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The paper demonstrates that by choosing unit‑quaternion coordinates, encrypted updates for variational quantum circuits become bilinear, allowing depth‑one homomorphic federated learning without bootstrapping. This coordinate choice reduces encrypted rotation updates to a single multiplicative level and federated averaging to zero levels, eliminating the previously prohibitive cost of one round per gate. Experiments across two cryptographic backends and up to 20 clients show negligible aggregation error and no measurable loss in utility, with hardware validation on a 156‑qubit processor achieving near‑optimal fidelity.

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