Christopher L. Baldwin

Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) are both instances of the same control problem in which a combination of two Hamiltonians is applied to minimize the energy of a quantum state. Previous work has suggested that the bang-bang structure of QAOA is optimal but with significant caveats, leaving open the question of what procedure is optimal in practice. In this work, we formalize the optimal control arguments proving that a time-constrained procedure has a bang at the beginning and end but can take on an annealing-like form in-between. In numerics on transverse field Ising models, we show that bang-anneal-bang procedures are common with optimal time-constrained QAOA Trotterizing the annealing portion. We furthermore show an equivalence between different types of time-constraints in this style of problem. The optimal procedures we find are far removed from a monotonically changing adiabatic path in the short-time limit, but we show that as the allowed time increases, the adiabatic limit and intuition from adiabatic quantum computing apply.