AI RESEARCH
Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency
arXiv CS.LG
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ArXi:2605.05942v1 Announce Type: cross 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.