Fig. 6: Comparison of optimizers for fixed UCCSD ansätze.
From: Fast gradient-free optimization of excitations in variational quantum eigensolvers
The optimizers under consideration are ExcitationSolve (red), COBYLA (purple), Gradient descent (yellow), Adam (green), SPSA (blue) and BFGS (brown). The plots show the error of the VQE with respect to the Full Configuration Interaction (FCI) solution ∣EVQE − EFCI∣ over the number of energy evaluations for the molecules a H2, b \({{{{\rm{H}}}}_{3}}^{+}\), c LiH and d H2O in their respective equilibrium geometries. The light blue region signifies the chemical accuracy (10−3 Ha), while alternating vertical shadings mark full sweeps over all parameters. As each sweep incurs the same cost as a single gradient computation via the parameter-shift rule, gradient-based optimizers exhibit piecewise constant progress in comparison. The BFGS optimizer needs additional energy evaluations per update step to approximate the Hessian. Therefore, the BFGS updates do not align with the vertical shadings.
