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In variational quantum algorithms the parameters of a parameterized quantumcircuit are optimized in order to minimize a cost function that encodes thesolution of the problem. The barren plateau phenomenon manifests as anexponentially vanishing dependence of the cost function with respect to thevariational parameters, and thus hampers the optimization process. We discusshow, and in which sense, the phenomenon of noise-induced barren plateausemerges in parameterized quantum circuits with a layered noise model. Previousresults have shown the existence of noise-induced barren plateaus in thepresence of local Pauli noise [arXiv:2007.14384]. We extend these resultsanalytically to arbitrary completely-positive trace preserving maps in twocases: 1) when a parameter-shift rule holds, 2) when the parameterized quantumcircuit at each layer forms a unitary $2$-design. The second example shows howhighly expressive unitaries give rise not only to standard barren plateaus[arXiv:1803.11173], but also to noise-induced ones. In the second part of thepaper, we study numerically the emergence of noise-induced barren plateaus inQAOA circuits focusing on the case of MaxCut problems on $d$-regular graphs andamplitude damping noise.

Emergence of noise-induced barren plateaus in arbitrary layered noise models