Fleming-Viot helps speed up variational quantum algorithms in the presence of barren plateaus
arxiv(2023)
摘要
Inspired by the Fleming-Viot stochastic process, we propose a parallel
implementation of variational quantum algorithms with the aim of helping the
algorithm get out of barren plateaus, where optimization direction is unclear.
In the Fleming-Viot tradition, parallel searches are called particles. In our
proposed approach, the search by a Fleming-Viot particle is stopped when it
encounters a region where the gradient is too small or noisy, suggesting a
barren plateau area. The stopped particle continues the search after being
regenerated at another location of the parameter space, potentially taking the
exploration away from barren plateaus. We first analyze the behavior of the
Fleming-Viot particles from a theoretical standpoint. We show that, when
simulated annealing optimizers are used as particles, the Fleming-Viot system
is expected to find the global optimum faster than a single simulated annealing
optimizer, with a relative efficiency that increases proportionally to the
percentage of barren plateaus in the domain. This result is backed up by
numerical experiments carried out on synthetic problems as well as on instances
of the Max-Cut problem, which show that our method performs better than plain
simulated annealing when large barren plateaus are present in the domain.
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