Exponential rise of dynamical complexity in quantum computing through projections

Daniel Klaus Burgarth (), Paolo Facchi, Vittorio Giovannetti, Hiromichi Nakazato, Saverio Pascazio and Kazuya Yuasa
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Daniel Klaus Burgarth: Institute of Mathematics, Physics and Computer Science, Aberystwyth University
Paolo Facchi: Università di Bari
Vittorio Giovannetti: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR
Hiromichi Nakazato: Waseda University
Saverio Pascazio: Università di Bari
Kazuya Yuasa: Waseda University

Nature Communications, 2014, vol. 5, issue 1, 1-6

Abstract: 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.

Date: 2014
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DOI: 10.1038/ncomms6173

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