Fast gradient-free optimization of excitations in variational quantum eigensolvers

Finding molecular ground states and energies with variational quantum eigensolvers is central to chemistry applications on quantum computers. Physically motivated ans\"atze based on excitation operators respect physical symmetries, but existing quantum-aware optimizers, such as Rotosolve, have been limited to simpler operator types. To fill this gap, we introduce ExcitationSolve, a fast quantum-aware optimizer that is globally-informed, gradient-free, and hyperparameter-free. ExcitationSolve extends these optimizers to parameterized unitaries with generators $G$ of the form $G^3=G$ exhibited by excitation operators in approaches such as unitary coupled cluster. ExcitationSolve determines the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for one update step. We provide optimization strategies for both fixed and adaptive variational ans\"atze, along with generalizations for simultaneously selecting and optimizing multiple excitations. On molecular ground state energy benchmarks, ExcitationSolve outperforms state-of-the-art optimizers by converging faster, achieving chemical accuracy for equilibrium geometries in a single parameter sweep, yielding shallower adaptive ans\"atze and remaining robust to real hardware noise. By uniting physical insight with efficient optimization, ExcitationSolve paves the way for scalable quantum chemistry calculations.