Fig. 9: Benchmarks on NISQ (ibm_quebec) quantum processor for fixed UCCSD ansätze.
From: Fast gradient-free optimization of excitations in variational quantum eigensolvers
The molecules a H2 and b \({{{{\rm{H}}}}_{3}}^{+}\) are studied, analogous to the simulated experiments in Fig. 6a, b, respectively. The optimizers considered are ExcitationSolve (red), Gradient descent (yellow), and COBYLA (purple), where the latter was discarded from the \({{{{\rm{H}}}}_{3}}^{+}\) experiments. Per optimizer, five experiments are performed out of which the best run (dashed), along with the mean (solid) and 95% confidence intervals (bands), are presented in terms of the VQE energy with respect to the Full Configuration Interaction (FCI) solution ∣EVQE − EFCI∣. While all presented optimizations exclusively rely on energy value (and gradient) information extracted from the the NISQ device ibm_quebec, the FCI errors shown are based on exact re-evaluations via state vector simulation for a clear quality assessment. Triangles instead represent such ibm_quebec energy estimates in the final ExcitationSolve parameter configuration (star), with shot counts from 1× (light red) to 10× (dark red) of the 8192 default. The inset plots also show the noisy energy values (red crosses) and compare the resulting energy reconstructions fθ( ⋅ ) (red) as used by ExcitationSolve with the exact energy function (black). The light blue background signifies chemical accuracy. Vertical lines mark the iterations in ExcitationSolve and GD.
