Title | Optimal Protocols in Quantum Annealing and QAOA Problems |

Publication Type | Journal Article |

Year of Publication | 2020 |

Authors | Brady, LT, Baldwin, CL, Bapat, A, Kharkov, Y, Gorshkov, AV |

Date Published | 3/19/2020 |

Abstract | 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. |

URL | https://arxiv.org/abs/2003.08952 |