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Exploring the quantum speed limit with computer games

Nature volume 532, pages 210–213 (2016)Cite this article

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A Retraction to this article was published on 22 July 2020

An Addendum to this article was published on 05 May 2020

Abstract

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies1,2. 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 Foldit3, EteRNA4 and EyeWire5 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 computing6. 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)7,8,9. Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

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Figure 1: The BringHomeWater challenge as seen by the player.
Figure 2: Fidelities of the transport problem for different solution durations.
Figure 3: Shovelling and tunnelling clans.
Figure 4: Optimization landscapes.

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References

  1. McLeod, P. & Dienes, Z. Do fielders know where to go to catch the ball or only how to get there? J. Exp. Psychol. Hum. Percept. Perform. 22, 531–543 (1996)

    Article  Google Scholar 

  2. Gigerenzer, G. & Todd, P. in Simple Heuristics That Make Us Smart (eds Gigerenzer, G., Todd, P. & The ABC Research Group) 3–34 (Oxford Univ. Press, 1999)

  3. Cooper, S. et al. Predicting protein structures with a multiplayer online game. Nature 466, 756–760 (2010)

    Article  ADS  CAS  Google Scholar 

  4. Lee, J. et al. RNA design rules from a massive open laboratory. Proc. Natl Acad. Sci. USA 111, 2122–2127 (2014)

    Article  ADS  Google Scholar 

  5. Kim, J. S. et al. Space-time wiring specificity supports direction selectivity in the retina. Nature 509, 331–336 (2014)

    Article  CAS  Google Scholar 

  6. Weitenberg, C., Kuhr, S., Mølmer, K. & Sherson, J. Quantum computation architecture using optical tweezers. Phys. Rev. A 84, 032322 (2011)

    Article  ADS  Google Scholar 

  7. Mandelstam, L. & Tamm, I. The uncertainty relation between energy and time in non-relativistic quantum mechanics. J. Phys. 9, 249–254 (1945)

    MathSciNet  MATH  Google Scholar 

  8. Caneva, T., Calarco, T., Fazio, R., Santoro, G. E. & Montangero, S. Speeding up critical system dynamics through optimized evolution. Phys. Rev. A 84, 012312 (2011)

    Article  ADS  Google Scholar 

  9. Gajdacz, M., Das, K. K., Arlt, J., Sherson, J. F. & Opatrný, T. Time limited optimal dynamics beyond the quantum speed limit. Phys. Rev. A 92, 062106 (2015)

    Article  ADS  Google Scholar 

  10. Monroe, C. Quantum information processing with atoms and photons. Nature 416, 238–246 (2002)

    Article  ADS  CAS  Google Scholar 

  11. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007)

    Article  ADS  Google Scholar 

  12. Devitt, S. J., Munro, W. J. & Nemoto, K. Quantum error correction for beginners. Rep. Prog. Phys. 76, 076001 (2013)

    Article  ADS  Google Scholar 

  13. Rabitz, H., Hsieh, M. M. & Rosenthal, C. M. Quantum optimally controlled transition landscapes. Science 303, 1998–2001 (2004)

    Article  ADS  CAS  Google Scholar 

  14. Sklarz, S. & Tannor, D. Loading a Bose-Einstein condensate onto an optical lattice: an application of optimal control theory to the nonlinear Schrödinger equation. Phys. Rev. A 66, 053619 (2002)

    Article  ADS  Google Scholar 

  15. Ugray, Z. et al. Scatter search and local NLP solvers: a multistart framework for global optimization. Inf. J. Comp. 19, 328–340 (2007)

    Article  MathSciNet  Google Scholar 

  16. Caneva, T. et al. Optimal control at the quantum speed limit. Phys. Rev. Lett. 103, 240501 (2009)

    Article  ADS  CAS  Google Scholar 

  17. Bilalić, M., Langner, R., Erb, M. & Grodd, W. Mechanisms and neural basis of object and pattern recognition: a study with chess experts. J. Exp. Psychol. Gen. 139, 728–742 (2010)

    Article  Google Scholar 

  18. Lintott, C. et al. Galaxy Zoo 1: data release of morphological classifications for nearly 900,000 galaxies. Mon. Not. R. Astron. Soc. 410, 166–178 (2011)

    Article  ADS  Google Scholar 

  19. Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010)

    Article  ADS  CAS  Google Scholar 

  20. Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010)

    Article  ADS  CAS  Google Scholar 

  21. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010)

    Article  ADS  CAS  Google Scholar 

  22. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011)

    Article  ADS  CAS  Google Scholar 

  23. Kaufman, A. et al. Entangling two transportable neutral atoms via local spin exchange. Nature 527, 208–211 (2015)

    Article  ADS  CAS  Google Scholar 

  24. De Chiara, G. et al. Optimal control of atom transport for quantum gates in optical lattices. Phys. Rev. A 77, 052333 (2008)

    Article  ADS  Google Scholar 

  25. Jäger, G., Reich, D. M., Goerz, M. H., Koch, C. P. & Hohenester, U. Optimal quantum control of Bose–Einstein condensates in magnetic microtraps: comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes. Phys. Rev. A 90, 033628 (2014)

    Article  ADS  Google Scholar 

  26. Doria, P., Calarco, T. & Montangero, S. Optimal control technique for many-body quantum dynamics. Phys. Rev. Lett. 106, 190501 (2011)

    Article  ADS  Google Scholar 

  27. Caneva, T., Calarco, T. & Montangero, S. Chopped random-basis quantum optimization. Phys. Rev. A 84, 022326 (2011)

    Article  ADS  Google Scholar 

  28. Zahedinejad, E., Schirmer, S. & Sanders, B. C. Evolutionary algorithms for hard quantum control. Phys. Rev. A 90, 032310 (2014)

    Article  ADS  Google Scholar 

  29. Roslund, J. & Rabitz, H. Experimental quantum control landscapes: inherent monotonicity and artificial structure. Phys. Rev. A 80, 013408 (2009)

    Article  ADS  Google Scholar 

  30. Vuculescu, O. & Bergenholtz, C. How to solve problems with crowds: a computer-based simulation model. Creativity Innov. Manage. 23, 121–136 (2014)

    Article  Google Scholar 

  31. Lieberoth, A. et al. Getting humans to do quantum optimization—user acquisition, engagement and early results from the citizen cyberscience game Quantum Moves. Human Comput. 1, 221–246 (2014)

    Article  Google Scholar 

  32. Sauermann, H. & Franzoni, C. Crowd science user contribution patterns and their implications. Proc. Natl Acad. Sci. USA 112, 679–684 (2015)

    Article  ADS  CAS  Google Scholar 

  33. Calarco, T., Dorner, U., Julienne, P., Williams, C. & Zoller, P. Quantum computations with atoms in optical lattices: marker qubits and molecular interactions. Phys. Rev. A 70, 012306 (2004)

    Article  ADS  Google Scholar 

  34. Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007)

    Article  ADS  CAS  Google Scholar 

  35. Jørgensen, N. B., Bason, M. G. & Sherson, J. F. One- and two-qubit quantum gates using superimposed optical-lattice potentials. Phys. Rev. A 89, 032306 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank the Quantum Moves players, without whom this work would have been impossible. We thank J. Rafner for graphical support and J. Jarecki, O. Vuculescu and C. Bergenholtz for discussions. This work was supported by the European Research Council, the Lundbeck Foundation, the Aarhus University Research Foundation, the Templeton Foundation, the Danish Council for Independent Research, the Villum Foundation and the Carlsberg Foundation.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark

    Jens Jakob W. H. Sørensen, Mads Kock Pedersen, Michael Munch, Pinja Haikka, Jesper Halkjær Jensen, Tilo Planke, Morten Ginnerup Andreasen, Miroslav Gajdacz, Klaus Mølmer, Andreas Lieberoth & Jacob F. Sherson

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  1. Jens Jakob W. H. Sørensen
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Contributions

All authors contributed to the construction of the online game platform and the effort to enlist users. J.J.W.H.S., M.K.P., T.P., M.G.A., M.G., K.M. and J.F.S. participated in the numerical analysis of the player and computer results. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Jacob F. Sherson.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Deviations from sin2(•) behaviour.

Colouring as in Fig. 2. a, The fidelity as a function of duration for the optimal families rescaled by the apparent QSL. The TQSL is found for each solution by fitting sin2(aT + b) where a and b are fitting parameters. The black line shows sin2(π/2T) for reference. The inset shows the infidelity (1 − F) as a function of duration close to the . b, The direct Hilbert velocity 〈Q〉T for the best solutions found by the HILO (purple), tunnelling (yellow) and shovelling (blue) clans respectively. Note that 〈Q〉T is only defined for durations with F < 1, so the curves end at different durations. The varying direct Hilbert velocity explains the deviation from in a.

Extended Data Figure 2 The reachability plot for Fig. 3a.

The distance between subsequent solutions as calculated by equation (1) in a list sorted according to the pairwise distance between solutions. The index is the position of the solutions in the list. Valleys identify closely spaced solutions, denoted clans. The valleys corresponding to tunnelling and shovelling clans are marked with yellow and blue respectively. The black line marks the threshold for the distance between consecutive solutions in a clan at 0.05.

Extended Data Figure 3 Solutions from CHOP and HILO.

The amplitude and the position of the tweezer as a function of time for the best player solutions in the tunnelling (yellow) and shovelling (blue) clans and the best HILO (purple). The dashed purple line shows the initial seed used by the best HILO solution (note that the dashed and solid purple lines in the top panel overlap). The total duration is T = 0.15.

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Supplementary information

Supplementary Information

The initial version of Quantum Moves: This .jar version includes all the levels used in the original Quantum Moves, on which the results presented here are based. For the new and improved version of Quantum Moves, see http://www.scienceathome.org (ZIP 20131 kb)

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Sørensen, J., Pedersen, M., Munch, M. et al. Exploring the quantum speed limit with computer games. Nature 532, 210–213 (2016). https://doi.org/10.1038/nature17620

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