IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA.
Phys Rev E. 2019 Jan;99(1-1):013304. doi: 10.1103/PhysRevE.99.013304.
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum-classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.
近期关于量子计算机近期应用的文献中包含了几个混合量子-经典变分方法应用的例子。该方法可应用于各种优化问题，但其实践性能尚未得到很好的研究。本文在寻找经典组合优化问题的解决方案的背景下，朝着刻画该方法实践性能的方向迈出了一些步骤。我们的研究基于通过几种经典非线性优化算法对六个组合优化问题的哈密顿量进行数值结果，实验是通过对 Qiskit 中实现的量子电路进行无噪声的经典模拟进行的。我们通过实验验证了以下几点：（1）对于具有许多 Pauli 项的哈密顿量，找到基态更难；（2）由于能够避免众多局部最优解，经典全局优化方法比局部方法更成功；（3）在变分形式中引入纠缠似乎没有明显的优势。
