Optimization schedules for the quantum approximate optimization algorithm

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm devised in 2014 in order to solve variational problems, typically in the field of quantum many body theory. Such kind of algorithms are made out of two components: a parameterized quantum circuit, whose role is to prepare the quantum state of a complex system, and a classical optimization algorithm, whose role is, instead, to locate the optimal parameters which minimize (or maximize, depending on the problem) a given cost function. Several studies have been performed with the idea of developing new optimization schedules and parameters initialization strategies in order to speed up the optimization procedure and increase its probability of success. In those studies, the QAOA has been applied to a classical problem, namely the MaxCut. In this work, we test optimization algorithms and initialization strategies for the QAOA applied to the ground state preparation of the Ising model with transverse magnetic field, a well-known many body model, in order to search for the schedule which performs the best among all others, i.e. which is capable to correctly identify the ground state of the model with the smallest effort in terms of computational resources. We focused on the INTERP initialization strategy coupled with local optimizers. We found that the L-BFGS-B local optimizer is the best optimization algorithm which, together with INTERP and properly-designed quantum circuits, is able to always locate the optimal parameters, finding the ground state of the model. We also implemented the transferability protocol which allow us to speed-up the computation and we provided a modified version of the INTERP strategy, tailored for the Ising model