Same Spectrum, Harder First-Order Training: Phase-Locking in Single- versus Multi-Qubit Re-Uploading Circuits

The paper compares single‑qubit re‑uploading (serial) variational quantum circuits with multi‑qubit circuits that use the same encoding budget for one‑dimensional inputs. It shows that although a serial circuit can represent any function a multi‑qubit circuit can, its first‑order training is more costly because all parameters move the state along a single phase‑locking direction, limiting the number of effective tangent directions. Experiments demonstrate that for larger encoding budgets the serial circuit converges far less often than the multi‑qubit control, and its held‑out error can be up to 1.5 times higher under Adam optimization.

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