Fig. 4: Alternating Layered Ansatz for V(θ) employed in our numerical simulations.
From: Cost function dependent barren plateaus in shallow parametrized quantum circuits
Each layer is composed of control-Z gates acting on alternating pairs of neighboring qubits which are preceded and followed by single qubit rotations around the y-axis, \({R}_{y}({\theta }_{i})={e}^{-i{\theta }_{i}{\sigma }_{y}/2}\). Shown is the case of two layers, nA = 1, and nB = 10 qubits. The number of variational parameters and gates scales linearly with nB: for the case shown there are 71 gates and 51 parameters. While each block in this ansatz will not form an exact local 2-design, and hence does not fall under our theorems, one can still obtain a cost-function-dependent barren plateau.
