  We report on two major hybrid applications of quantum computing, namely, the
quantum approximate optimisation algorithm (QAOA) and the variational quantum
eigensolver (VQE). Both are hybrid quantum classical algorithms as they require
incremental communication between a classical central processing unit and a
quantum processing unit to solve a problem. We find that the QAOA scales much
better to larger problems than random guessing, but requires significant
computational resources. In contrast, a coarsely discretised version of quantum
annealing called approximate quantum annealing (AQA) can reach the same
promising scaling behaviour using much less computational resources. For the
VQE, we find reasonable results in approximating the ground state energy of the
Heisenberg model when suitable choices of initial states and parameters are
used. Our design and implementation of a general quasi-dynamical evolution
further improves these results.
