Improved QOCA ansatz using an adapt-VQE approach

One of the most promising applications of quantum computers in the NISQ era is quantum simulation, especially using variational quantum algorithms. The implementation, as well as the convergence of those algorithms, are however highly dependent on the choice of circuit ansatz. One example is the Quantum Optimal Control inspired Ansatz [Choquette et al. (2021)] where circuits constitute of two blocks: one that encodes the problem Hamiltonian, taking into account the symetries of the problem, and a second block which purposely break the symetries of the problem in hope of finding shortcuts in the Hilbert space. It performs well when applied to the Fermi Hubbard model and H20 compared to other well-established. However some questions remained unanswered: what are the drive terms that matter and how should they be ordered? Can we make the circuits shallower? In this talk we address these questions and show that the circuit depth and the number of CNOTs can be reduce by combining the QOCA ansatz with the adaptive method adapt-VQE [Grimsley et al. (2019)].