Noncyclic geometric changes of quantum states
2006 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 74, no 2, 022106- p.Article in journal (Refereed) Published
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.
Place, publisher, year, edition, pages
2006. Vol. 74, no 2, 022106- p.
Non-Abelian geometric phase, quantum holonomy, quantum computation
Research subject Physics
IdentifiersURN: urn:nbn:se:uu:diva-96147DOI: 10.1103/PhysRevA.74.022106ISI: 000240238300017OAI: oai:DiVA.org:uu-96147DiVA: diva2:170624