Optimised counderdiabatic driving with additional terms

Counterdiabatic driving protocols provide a way to speed up adiabatic dynamics. In principle, they allow us to bypass typical adiabatic limitations like slow driving rates and suppress excitations into unwanted states. These protocols can be utilised to implement arbitrarily fast quantum annealing. However, the usual approaches to counterdiabatic driving require the knowledge of the eigenstates of the system, which limits their application. It has recently been shown that the need to know the systems solutions can be removed by using a variational approach [D Sels and A Polkovnikov, PNAS 114 (20), E3909 (2017)]. We couple such a protocol with new additional parametrised driving terms and optimise the enhanced driving. We apply this new approach to random graph problems encoded in spin Hamiltonians, such as the maximum independent set and find a substantial improvement over naive adiabatic methods when optimising the additional driving terms. This new protocol allows us to improve solutions to the MIS problem, while heralding promising applications in other near-term quantum technologies.