Fig. 5: 1D ExcitationSolve with coordinate descent vs. 2D ExcitationSolve.
From: Fast gradient-free optimization of excitations in variational quantum eigensolvers
The simultaneous optimization of two parameters can be achieved either by effectively reducing it to a 1D optimization task using coordinate descent or employing a true 2D optimization based on the energy landscape from Eq. (8). Color indicates energy linearly from low (violet) to high (yellow). In this example, no matter which parameter is tuned first, the 1D coordinate descent approach (white arrows) converges only to a local minimum (black star marker). Also, this convergence takes up multiple iterations. Meanwhile, in the proper 2D case, the global reconstruction of the 2D second-order Fourier series permits an immediate jump (black arrow) to the global minimum (white star marker).
