  One of the most promising attempts towards solving optimization problems with
quantum computers in the noisy intermediate scale era of quantum computing are
variational quantum algorithms. The Quantum Alternating Operator Ansatz
provides an algorithmic framework for constrained, combinatorial optimization
problems. As opposed to the better known standard QAOA protocol, the
constraints of the optimization problem are built into the mixing layers of the
ansatz circuit, thereby limiting the search to the much smaller Hilbert space
of feasible solutions. In this work we develop mixing operators for a wide
range of scheduling problems including the flexible job shop problem. These
mixing operators are based on a special control scheme defined by a constraint
graph model. After describing an explicit construction of those mixing
operators, they are proven to be feasibility preserving, as well as exploring
the feasible subspace.
