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Phys. Rev. A 79, 060305(R) (2009) [4 pages]

Local controllability of quantum networks

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Daniel Burgarth1, Sougato Bose2, Christoph Bruder3, and Vittorio Giovannetti4
1Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford OX1 3LB, United Kingdom
2Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
3Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
4NEST CNR–INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy

Received 30 May 2008; revised 13 February 2009; published 15 June 2009

We give a sufficient criterion that guarantees that a many-body quantum system can be controlled by properly manipulating the (local) Hamiltonian of one of its subsystems. The method can be applied to a wide range of systems: it does not depend on the details of the couplings but only on their associated topology. As a special case, we prove that Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the spins at their ends. In principle, arbitrary quantum algorithms can be performed on such chains by acting on a single qubit.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.79.060305
DOI:
10.1103/PhysRevA.79.060305
PACS:
03.67.Lx, 89.75.Hc
 
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