dorsal/arxiv
View SchemaNon-Abelian Berry connections for quantum computation
| Authors | Jiannis Pachos, Paolo Zanardi, Mario Rasetti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9907103 |
| URL | https://arxiv.org/abs/quant-ph/9907103 |
| DOI | 10.1103/PhysRevA.61.010305 |
| Journal | Phys.Rev. A61 (2000) 010305 |
Abstract
In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible, for a specific model, to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multi-partite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.
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"abstract": "In the holonomic approach to quantum computation information is encoded in a\ndegenerate eigenspace of a parametric family of Hamiltonians and manipulated by\nthe associated holonomic gates. These are realized in terms of the non-abelian\nBerry connection and are obtained by driving the control parameters along\nadiabatic loops. We show how it is possible, for a specific model, to\nexplicitly determine the loops generating any desired logical gate, thus\nproducing a universal set of unitary transformations. In a multi-partite system\nunitary transformations can be implemented efficiently by sequences of local\nholonomic gates. Moreover a conceptual scheme for obtaining the required\nHamiltonian family, based on frequently repeated pulses, is discussed, together\nwith a possible process whereby the initial state can be prepared and the final\none can be measured.",
"arxiv_id": "quant-ph/9907103",
"authors": [
"Jiannis Pachos",
"Paolo Zanardi",
"Mario Rasetti"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.61.010305",
"journal_ref": "Phys.Rev. A61 (2000) 010305",
"title": "Non-Abelian Berry connections for quantum computation",
"url": "https://arxiv.org/abs/quant-ph/9907103"
},
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