Multi-Angle Quantum Approximate Optimization Algorithm for Qutrits

Qutrits have been shown to solve combinatorial optimization problems such as Max-$3$-Cut by using formulations of the Quantum Approximate Optimization Algorithm (QAOA). In this work, we will extend QAOA for qutrits to the multi-angle setting, where each gate in the cost and mixing unitaries are parameterized by a possibly unique angle. We present three multi-angle strategies, the ``full'' strategy with each gate having a unique angle, the ``term'' strategy where gates in the same term of the unitary share an angle, and the ``subspace'' strategy where gates that rotate in the same two-dimensional subspace share an angle. We test these multi-angle strategies on the Max-$3$-Cut problem and show that each strategy performs better than normal QAOA for qutrits, with the ``full'' strategy performing the best.