title: Exponential rise of dynamical complexity in quantum computing through projections.
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.
authors.affiliation: Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK.
authors.forename: Daniel Klaus
authors.initials: DK
authors.lastname: Burgarth
authors.affiliation: 1] Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy [2] INFN, Sezione di Bari, I-70126 Bari, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Facchi
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Giovannetti
authors.affiliation: Department of Physics, Waseda University, Tokyo 169-8555, Japan.
authors.forename: Hiromichi
authors.initials: H
authors.lastname: Nakazato
authors.affiliation: 1] Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy [2] INFN, Sezione di Bari, I-70126 Bari, Italy.
authors.forename: Saverio
authors.initials: S
authors.lastname: Pascazio
authors.affiliation: Department of Physics, Waseda University, Tokyo 169-8555, Japan.
authors.forename: Kazuya
authors.initials: K
authors.lastname: Yuasa