Exploring the quantum speed limit with computer games
Authors: Morten Ginnerup Andreasen
Klaus Mølmer
Jacob F Sherson
Jesper Halkjær Jensen
Michael Munch
Pinja Haikka
Andreas Lieberoth
Jens Jakob W H Sørensen
Miroslav Gajdacz
Mads Kock Pedersen
Tilo Planke
Journal: Nature (2016)
Discipline: Multidisciplinary
Keywords: Citizen science; Gamification; Quantum physics; Heuristic strategies; Optimization problems
Affiliations: Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark.

Abstract:  Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond. 

Retracted: No

PubPeer comments:
 This article has an Expression of Concern:  The authors have alerted the editors of Nature to an error in the code underlying the work in this Letter, and have informed us that this error will have an impact on the conclusions that can reliably be drawn. Nature is working with the authors to resolve the matter, but in the meantime, readers are cautioned against using results from this Letter. https: www.nature.com articles s41586-020-2274-0 , 
 2020 retraction. https: doi.org 10.1038 s41586-020-2515-2 We, the authors, are regretfully retracting this Article owing to an error in our computer code that means the quantitative results reported are not valid. We thank A. Gru00f8nlund and D. Sels, whose independent efforts1,2 pointed to potential problems with our optimization algorithm. The error was identified by A. Gru00f8nlund, who has provided a detailed account3 of the error and its effect on the quantitative results in our Article. For more recent and comprehensive explorations of the performance differences between player-seeded and randomly seeded algorithms, we refer to our recent work4. References 1. Sels, D. Stochastic gradient ascent outperforms gamers in the Quantum Moves game. Phys. Rev. A 97, 040302 (2018) 2. Gru00f8nlund, A. Algorithms clearly beat gamers at Quantum Moves: a verification. Preprint at https: arXiv.org abs 1904.01008 (2019). 3. Gru00f8nlund, A. Explaining the poor performance of the KASS algorithm implementation. Preprint at https: arXiv.org abs 2003.05808 (2020). 4. Jensen, J. H. M. et al. Crowdsourcing human common sense for quantum control. Preprint at https: arXiv.org abs 2004.03296 (2020). ,