Noncyclic geometric changes of quantum states

Journal Article · Tue Aug 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.022106· OSTI ID:20853017

Kult, David; Sjoeqvist, Erik ^[1]; Aaberg, Johan ^[1]

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1. Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala (Sweden)

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.

• OSTI ID: 20853017
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ENERGY LEVELS
GATING CIRCUITS
QUANTUM COMPUTERS
QUANTUM MECHANICS
QUANTUM NUMBERS