Rapid quantum approximate solvers for combinatorial optimisation problems inspired by Hamiltonians for optimal state-transfer

Designing and developing quantum algorithms remains a formidable challenge without mature hardware to test ideas on. Here we suggest a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of this new design heuristic. We find this new approach gives a better approximation ratio than the Quantum Approximate Optimisation Algorithm at lowest depth on the majority of problem instances considered, while utilising comparable resources. This opens the door to investigating new approaches for tackling combinatorial optimisation problems, away from adiabatic inspired approaches.