  We present a highly efficient quantum circuit for performing continuous time
quantum walks (CTQWs) over an exponentially large set of combinatorial objects,
provided that the objects can be indexed efficiently. CTQWs form the core
mixing operation of a generalised version of the Quantum Approximate
Optimisation Algorithm, which works by `steering' the quantum amplitude into
high-quality solutions. The efficient quantum circuit holds the promise of
finding high-quality solutions to certain classes of NP-hard combinatorial
problems such as the Travelling Salesman Problem, maximum set splitting, graph
partitioning, and lattice path optimisation.
