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Exponential rise of dynamical complexity in quantum computing through projections

Author

Listed:
  • Daniel Klaus Burgarth

    (Institute of Mathematics, Physics and Computer Science, Aberystwyth University)

  • Paolo Facchi

    (Università di Bari
    INFN, Sezione di Bari)

  • Vittorio Giovannetti

    (NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR)

  • Hiromichi Nakazato

    (Waseda University)

  • Saverio Pascazio

    (Università di Bari
    INFN, Sezione di Bari)

  • Kazuya Yuasa

    (Waseda University)

Abstract

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

Suggested Citation

  • Daniel Klaus Burgarth & Paolo Facchi & Vittorio Giovannetti & Hiromichi Nakazato & Saverio Pascazio & Kazuya Yuasa, 2014. "Exponential rise of dynamical complexity in quantum computing through projections," Nature Communications, Nature, vol. 5(1), pages 1-6, December.
    • Handle: RePEc:nat:natcom:v:5:y:2014:i:1:d:10.1038_ncomms6173
    DOI: 10.1038/ncomms6173
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