dorsal/arxiv
View SchemaGeometric phase for SU(N) through fiber bundles and unitary integration
| Authors | D. B. Uskov, A. R. P. Rau |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511192 |
| URL | https://arxiv.org/abs/quant-ph/0511192 |
| DOI | 10.1103/PhysRevA.74.030304 |
| Journal | Phys.Rev.A74:030304,2006 |
Abstract
Geometric phases are important in quantum physics and now central to fault tolerant quantum computation. For spin-1/2 and SU(2), the Bloch sphere $S^2$, together with a U(1) phase, provides a complete SU(2) description. We generalize to $N$-level systems and SU($N$) in terms of a $2(N-1)$-dimensional base space and reduction to a ($N$-1)-level problem, paralleling closely the two-dimensional case. This iteratively solves the time evolution of an $N$-level system and gives ($N$-1) geometric phases explicitly. A complete analytical construction of a S^4 Bloch-like sphere for two qubits is given for the Spin(5) or SO(5) subgroup of SU(4).
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"abstract": "Geometric phases are important in quantum physics and now central to fault\ntolerant quantum computation. For spin-1/2 and SU(2), the Bloch sphere $S^2$,\ntogether with a U(1) phase, provides a complete SU(2) description. We\ngeneralize to $N$-level systems and SU($N$) in terms of a $2(N-1)$-dimensional\nbase space and reduction to a ($N$-1)-level problem, paralleling closely the\ntwo-dimensional case. This iteratively solves the time evolution of an\n$N$-level system and gives ($N$-1) geometric phases explicitly. A complete\nanalytical construction of a S^4 Bloch-like sphere for two qubits is given for\nthe Spin(5) or SO(5) subgroup of SU(4).",
"arxiv_id": "quant-ph/0511192",
"authors": [
"D. B. Uskov",
"A. R. P. Rau"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.030304",
"journal_ref": "Phys.Rev.A74:030304,2006",
"title": "Geometric phase for SU(N) through fiber bundles and unitary integration",
"url": "https://arxiv.org/abs/quant-ph/0511192"
},
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