dorsal/arxiv
View SchemaFour-level and two-qubit systems, sub-algebras, and unitary integration
| Authors | A. R. P. Rau, G. Selvaraj, D. Uskov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501048 |
| URL | https://arxiv.org/abs/quant-ph/0501048 |
| DOI | 10.1103/PhysRevA.71.062316 |
| Journal | Phys.Rev.A71:062316,2005 |
Abstract
Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.
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"abstract": "Four-level systems in quantum optics, and for representing two qubits in\nquantum computing, are difficult to solve for general time-dependent\nHamiltonians. A systematic procedure is presented which combines analytical\nhandling of the algebraic operator aspects with simple solutions of classical,\nfirst-order differential equations. In particular, by exploiting $su(2) \\oplus\nsu(2)$ and $su(2) \\oplus su(2) \\oplus u(1)$ sub-algebras of the full SU(4)\ndynamical group of the system, the non-trivial part of the final calculation is\nreduced to a single Riccati (first order, quadratically nonlinear) equation,\nitself simply solved. Examples are provided of two-qubit problems from the\nrecent literature, including implementation of two-qubit gates with Josephson\njunctions.",
"arxiv_id": "quant-ph/0501048",
"authors": [
"A. R. P. Rau",
"G. Selvaraj",
"D. Uskov"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.062316",
"journal_ref": "Phys.Rev.A71:062316,2005",
"title": "Four-level and two-qubit systems, sub-algebras, and unitary integration",
"url": "https://arxiv.org/abs/quant-ph/0501048"
},
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