Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency
Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical frequency redundancy, and require the same minimum parameter count for coefficient control. Despite this equivalence, trainability varies substantially with architecture shape $(N,L)$ at fixed $E$. We identify structural rank deficiency of the coefficient matching Jacobian $J$ as the mechanism responsible. For serial single-qubit architectures, we prove $\mathrm{rank}(J) \leq 2L+1$ regardless of parameter count $P$, with $\dim(\ker J) \geq P-(2L+1)$ gr...
| Authors | Michael Poppel, David Bucher, Maximilian Zorn et al. |
|---|---|
| Primary category | quant-ph |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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