Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks
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 $\mathrm{SU(2)}$ 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...
| Authors | Marcel Mordarski, Nathan Mani, Arshad Patel et al. |
|---|---|
| Primary category | quant-ph |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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