Hidden time-evolution structure of the quantum approximate optimization algorithm when it is used for ground-state preparation*

The quantum approximate optimization algorithm (QAOA) has emerged as an accurate and efficient approach to solve many optimization problems on quantum computers including ground-state preparation. The algorithm has many similarities to Trotterized time evolution. For example, one way to envision how it works is that it uses large inhomogenous time steps plus an additional variational principle to correct for the Trotter errors. By comparing optimized QAOA trajectories, we find it is closely related to local adiabatic time evolution. We then modify a Trotterized time evolution (based on the local adiabatic field) by adding in a variational scaling of the Hamiltonian at each time step. We achieve very high accuracy (fidelities of better than five 9s) with this approach. Our concrete example works with the transverse-field Ising model, but we believe the principles uncovered here are much more general and widely applicable.