Natural evolution strategies and variational Monte Carlo

A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. The recent work of Gomes et al (2019 arXiv:1910.10675) on heuristic combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies (NES). The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular, it is found that NES can achieve approximation ratios competitive with widely used heuristic algorithms for Max-Cut, at the expense of increased computation time.

Automated summary

The concept of quantum natural evolution strategies is introduced, which combines known quantum/classical algorithms for classical black-box optimization. The work by Gomes et al (2019 arXiv:1910.10675) highlights the connection between neural quantum states and natural evolution strategies (NES) in heuristic combinatorial optimization, showing a systematic strategy for improving approximation ratios. It is found that NES can achieve competitive approximation ratios for Max-Cut with commonly used heuristic algorithms, albeit with increased computation time.