Exhaustive and feasible parametrisation with applications to the travelling salesperson problem

Understand

This paper introduces the concept of exhaustively parametrised, feasibility-respecting quantum circuits for constrained combinatorial optimisation problems.

• Such circuits can reach, given the right parameter values, every feasible solution with certainty -- including the optimum -- with a fixed number of parameters, while avoiding infeasible solutions altogether.
• This is in sharp contrast to conventional quantum alternating operator ansatz schemes, which are merely guaranteed to reach the optimum asymptotically.
• We introduce an abstract pipeline for constructing exhaustively parametrised, feasibility-respecting circuits from a transitive group action on a problem's feasible set.