dorsal/arxiv
View SchemaChow's theorem and universal holonomic quantum computation
| Authors | Dennis Lucarelli |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111078 |
| URL | https://arxiv.org/abs/quant-ph/0111078 |
| DOI | 10.1088/0305-4470/35/24/309 |
| Journal | J. Phys. A: Math. Gen. 35:5107 (2002) |
Abstract
A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a universal two-qubit logic gate is attainable for this model.
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"abstract": "A theorem from control theory relating the Lie algebra generated by vector\nfields on a manifold to the controllability of the dynamical system is shown to\napply to Holonomic Quantum Computation. Conditions for deriving the holonomy\nalgebra are presented by taking covariant derivatives of the curvature\nassociated to a non-Abelian gauge connection. When applied to the Optical\nHolonomic Computer, these conditions determine that the holonomy group of the\ntwo-qubit interaction model contains $SU(2) \\times SU(2)$. In particular, a\nuniversal two-qubit logic gate is attainable for this model.",
"arxiv_id": "quant-ph/0111078",
"authors": [
"Dennis Lucarelli"
],
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"quant-ph"
],
"doi": "10.1088/0305-4470/35/24/309",
"journal_ref": "J. Phys. A: Math. Gen. 35:5107 (2002)",
"title": "Chow\u0027s theorem and universal holonomic quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0111078"
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