Research
Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks
arXiv:2609.30581v1 Announce Type: cross Abstract: Encrypted training relies on keeping server-side updates low-degree. This constraint traditionally excludes models whose weights inhabit a compact Lie
arXiv:2609.30581v1 Announce Type: cross Abstract: Encrypted training relies on keeping server-side updates low-degree. This constraint traditionally excludes models whose weights inhabit a compact Lie group (notably variational quantum circuits, where every trainable weight is an SU(2) rotation). Expressed in Euler angles or discrete alphabets, these updates appear transcendental, historically demanding prohibitive costs: one client--server round per gate, or upwards of 25{,}000 operations per weight. This penalty is strictly an artefact of coordinates. In the unit-quaternion (spin) chart, group composition is exactly bilinear (degree two, with coefficients in {-1,0,+1}). Consequently, encrypted rotation updates cost one multiplicative level and federated averaging costs zero in any levelled homomorphic scheme, completely eliminating bootstrapping. This implementation-independent algebraic property is confirmed across two cryptographic backends, introducing only 0.0 and -2.0imes10^{-12} rad of aggregation error. Leveraging this reduction yields a non-interactive protocol for encrypted federated training of hybrid quantum--classical networks. It includes correctness proofs for aggregation and sign handling, plus a compilation lemma proving parameterised entanglers add only constant-factor overhead without altering the depth class. Empirically, a paired five-seed study confirms zero measurable utility tax (Delta=+9imes10^{-6} MSE, p=0.92), and a noise-budget ablation falsifies the hypothesis that encryption noise regularises. These convergence trends replicate across datasets and scale to 20 clients. Finally, hardware validation on a 156-qubit processor achieves 0.9918 fidelity against a 0.99957 unencrypted control.
Related
- DisAgg: Distributed Aggregators for Efficient Secure Aggregation in Federated Learning
- Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels
- Towards Deep Encrypted Training: Low-Latency, Memory-Efficient, and High-Throughput Inference for Privacy-Preserving Neural Networks
Source: arXiv cs.LG | 2026-09-28