Noise-induced shallow circuits and the absence of barren plateaus

A theoretical study proves that uncorrected local noise on quantum circuits — including non-unital noise models more realistic than depolarizing — effectively truncates circuit depth to O(log n) layers for the task of estimating observable expectation values. While non-unital noise provably avoids barren plateaus (gradients don't vanish), this is shown to be a consequence of only the final logarithmic-depth layers being trainable, not a sign of computational power. An efficient classical algorithm is derived that can estimate local observable expectation values to constant additive accuracy for any depth and architecture. The combined results suggest that noisy quantum circuits without carefully engineered noise exploitation are unlikely to outperform shallow circuits for variational quantum algorithms and quantum machine learning.