Optimal Protocols in Quantum Annealing and QAOA Problems

TitleOptimal Protocols in Quantum Annealing and QAOA Problems
Publication TypeJournal Article
Year of Publication2020
AuthorsBrady, LT, Baldwin, CL, Bapat, A, Kharkov, Y, Gorshkov, AV
Date Published3/19/2020

Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or "bang-bang") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. Through simulations of various transverse field Ising models, we demonstrate that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.