



01409nas a2200157   4500008004100000245006100041210006100102260001400163520091900177100002101096700002901117700002101146700002201167700002501189856003701214       2020                        eng d00aOptimal Protocols in Quantum Annealing and QAOA Problems0 aOptimal Protocols in Quantum Annealing and QAOA Problems  c3/19/20203 a<p>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 &quot;bang-bang&quot;) 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.</p>1 aBrady, Lucas, T.1 aBaldwin, Christopher, L.1 aBapat, Aniruddha1 aKharkov, Yaroslav1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2003.08952