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Quantum mechanics can reduce the complexity of classical models

Author

Listed:
  • Mile Gu

    (Centre for Quantum Technologies, National University of Singapore)

  • Karoline Wiesner

    (School of Mathematics, Centre for Complexity Sciences, University of Bristol)

  • Elisabeth Rieper

    (Centre for Quantum Technologies, National University of Singapore)

  • Vlatko Vedral

    (Centre for Quantum Technologies, National University of Singapore
    National University of Singapore
    Clarendon Laboratory, University of Oxford, Oxford OX1 3PU)

Abstract

Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. Here we show how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.

Suggested Citation

  • Mile Gu & Karoline Wiesner & Elisabeth Rieper & Vlatko Vedral, 2012. "Quantum mechanics can reduce the complexity of classical models," Nature Communications, Nature, vol. 3(1), pages 1-5, January.
    • Handle: RePEc:nat:natcom:v:3:y:2012:i:1:d:10.1038_ncomms1761
    DOI: 10.1038/ncomms1761
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    Cited by:

    1. Kang-Da Wu & Chengran Yang & Ren-Dong He & Mile Gu & Guo-Yong Xiang & Chuan-Feng Li & Guang-Can Guo & Thomas J. Elliott, 2023. "Implementing quantum dimensionality reduction for non-Markovian stochastic simulation," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    2. Convertino, Matteo & Annis, Antonio & Nardi, Fernando, 2019. "Information-theoretic Portfolio Decision Model for Optimal Flood Management," Earth Arxiv k5aut, Center for Open Science.

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