Progress towards Analytically Optimal Angles in Quantum Approximate Optimisation

The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on quantum processor and driven to convergence by classical outer loop optimisation. co-processor varies individual application times of problem/driver propagator sequence prepare state which approximately minimizes the problem's generator. Analytical solutions choose optimal (called angles) have proven difficult find, whereas optimisation resource intensive. Here we prove that parameters for $p=1$ layer reduce one free variable in thermodynamic limit, recover angles. We moreover demonstrate conditions vanishing gradients overlap function share similar form leads linear relation between circuit parameters, independent number qubits. Finally, present list numerical effects, observed particular system size depth, are yet be explained analytically.