Classical symmetries and the Quantum Approximate Optimization Algorithm

We study the relationship between Quantum Approximate Optimization Algorithm (QAOA) and underlying symmetries of objective function to be optimized. Our approach formalizes connection quantum symmetry properties QAOA dynamics group classical function. The is general includes but not limited problems defined on graphs. show a series results exploring highlight examples hard problem classes where nontrivial subgroup can obtained efficiently. In particular, we how lead invariant measurement outcome probabilities across states connected by such symmetries, independent choice algorithm parameters or number layers. To illustrate power developed connection, apply machine learning techniques toward predicting performance based considerations. provide numerical evidence that small set graph suffices predict minimum depth required achieve target approximation ratio MaxCut problem, in practically important setting parameter schedules are constrained linear hence easier optimize.