Constraint-Preserving QAOA for Personnel Rostering: Coverage-Preserving and Guarded-XY Mixer Constructions

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a promising framework for combinatorial optimization, but constrained problems are commonly handled using energetic penalty terms that require calibration and allow infeasible configurations to remain dynamically accessible. We develop a constraint-preserving QAOA framework for personnel rostering in which hard scheduling constraints are embedded directly into the mixer Hamiltonian. Using a binary rostering model with daily coverage and no-consecutive-duty constraints, we formulate the dynamics from a transition-graph perspective and introduce a guarded-XY mixer that confines the evolution to the fully feasible scheduling manifold. We further distinguish feasibility preservation from feasible-transition design and propose a tight-pattern extension that introduces collective feasible exchanges in saturated workload segments where local guarded exchanges alone are insufficient. Exact statevector simulations demonstrate that, compared with Penalty-X and Coverage-XY formulations under both expectation-value and Conditional Value-at-Risk optimization, the proposed approach eliminates hard-constraint penalty calibration, guarantees feasible evolution by construction, and consistently yields higher-quality output distributions with stronger concentration on optimal feasible schedules. To the best of our knowledge, this is the first constraint-preserving QAOA formulation for personnel rostering, and the transition-graph framework is readily applicable to a broad class of constrained quantum optimization problems.