Brady Lucas T, Baldwin Christopher L, Bapat Aniruddha, Kharkov Yaroslav, Gorshkov Alexey V
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2021 Feb 19;126(7):070505. doi: 10.1103/PhysRevLett.126.070505.
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 analytically 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. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.
量子退火（QA）和量子近似优化算法（QAOA）是以下控制问题的两种特殊情况：应用两个哈密顿量的组合来最小化量子态的能量。哪种方法更有效仍不明确。在此，我们通过解析应用最优控制理论框架表明，一般来说，在给定固定时间量的情况下，最优过程在开始和结束时具有QAOA的脉冲式（或“砰砰”式）结构，但在中间可以具有平滑的退火结构。这与之前认为砰砰式（即QAOA）协议是理想的工作形成对比。为了支持这项理论工作，我们对各种横向场伊辛模型进行了模拟，证明了砰砰 - 退火 - 砰砰协议更为常见。这里确定的一般特征为量子优化算法的新兴实验实现提供了指导。
