dorsal/arxiv
View SchemaNoncyclic geometric changes of quantum states
| Authors | David Kult, Johan Åberg, Erik Sjöqvist |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512045 |
| URL | https://arxiv.org/abs/quant-ph/0512045 |
| DOI | 10.1103/PhysRevA.74.022106 |
| Journal | Phys. Rev. A 74, 022106 (2006) |
Abstract
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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"abstract": "Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by\ngeometric properties of a quantum system, have been much under focus in the\nphysics community as generalizations of the Abelian Berry phase. Apart from\nbeing a general phenomenon displayed in various subfields of quantum physics,\nthe use of holonomies has lately been suggested as a robust technique to obtain\nquantum gates; the building blocks of quantum computers. Non-Abelian holonomies\nare usually associated with cyclic changes of quantum systems, but here we\nconsider a generalization to noncyclic evolutions. We argue that this open-path\nholonomy can be used to construct quantum gates. We also show that a structure\nof partially defined holonomies emerges from the open-path holonomy. This\nstructure has no counterpart in the Abelian setting. We illustrate the general\nideas using an example that may be accessible to tests in various physical\nsystems.",
"arxiv_id": "quant-ph/0512045",
"authors": [
"David Kult",
"Johan \u00c5berg",
"Erik Sj\u00f6qvist"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.022106",
"journal_ref": "Phys. Rev. A 74, 022106 (2006)",
"title": "Noncyclic geometric changes of quantum states",
"url": "https://arxiv.org/abs/quant-ph/0512045"
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