The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the algorithms ultimate limitations. Here we report that QAOA exhibits a strong dependence on a problem instances constraint to variable ratio−this problem density places a limiting restriction on the algorithms capacity to minimize a corresponding objective function (and hence solve optimization problem instances). Such reachabilitydeficits persist even in the absence of barren plateaus [McClean et al., 2018] and are outside of the recently reported level-1 QAOA limitations [Hastings 2019]. These findings are among the first to determine strong limitations on variational quantum approximate optimization.
@article{arxiv.1906.11259,
title = {Reachability Deficits in Quantum Approximate Optimization},
author = {V. Akshay and H. Philathong and M. E. S. Morales and J. Biamonte},
journal= {arXiv preprint arXiv:1906.11259},
year = {2020}
}