Noncyclic geometric changes of quantum states

Details Noncyclic geometric changes of quantum states Noncyclic geometric changes of quantum states

2005-12-06

arxiv.org/abs/quant-ph/0512045v2

Phys. Rev. A 74, 022106 (2006)

Physics

Quantum Physics

Extended version, new title, journal reference added

Scientific paper

10.1103/PhysRevA.74.022106

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.

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