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Nat Commun. 2014 Oct 10;5:5173. doi: 10.1038/ncomms6173.

Exponential rise of dynamical complexity in quantum computing through projections.

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Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK.
1] Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy [2] INFN, Sezione di Bari, I-70126 Bari, Italy.
NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy.
Department of Physics, Waseda University, Tokyo 169-8555, Japan.


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.

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