Algorithms Clearly Beat Gamers at Quantum Moves. A Verification. (arXiv:1904.01008v3 [cs.OH] UPDATED)

The paper [S{\o}rensen et al., Nature 532] presents and discusses results for
a Quantum Moves game, BringHomeWater, where players have attempted to move a
quantum state from one position to another in a simulated optical tweezer and
atoms setup. The paper compares the player solutions to numerical methods that
the authors discuss. In particular, [S{\o}rensen et al., Nature 532] show
evidence that the so-called Krotov optimization method performs worse than
solutions that the human players have come up with. Given the assumption that
the Krotov method has been correctly applied, the evidence points to the fact
that human players can outperform the Krotov method. This is the find and claim
of [S{\o}rensen et al., Nature 532] and it features prominent in the abstract
of the paper. It leads the authors to conclude that 'players succeed where
purely numerical optimization fails, and analysis of their solutions provide
insights into the problem of optimization of a more profound and general
nature.' While it seems clear from the presented data that human players have
indeed outperformed a particular implementation of the Krotov algorithm (and,
according to [S{\o}rensen et al., Nature 532], as a consequence also algorithms
like CRAB and evolutionary approaches which perform worse than Krotov), there
is no reason to believe that this finding is of any particular significance. In
fact, as has been discussed first by D. Sels [D. Sels, Phys. Rev. A 97,
040302], a very simple approach using classical arguments can capture the
BringHomeWater Quantum Moves game far better than the player approach.
Furthermore, as also shown by [D. Sels, Phys. Rev. A 97, 040302], one of the
simplest optimization algorithms available, Stochastic Ascent, can outperform
all of the above. Here we elaborate on the method discussed by [D. Sels, Phys.
Rev. A 97, 040302] and verify the conclusions put forward by D. Sels

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