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Four-level and two-qubit systems, sub-algebras, and unitary integration
A. R. P. Rau, G. Selvaraj, D. Uskov
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0501048
- categories:
- quant-ph
- comments:
- 1 gzip file with 1 tex and 9 eps figure files. Unpack with command:
gunzip RSU05.tar.gz
- doi:
- 10.1103/PhysRevA.71.062316
- arxiv_id:
- quant-ph/0501048
- journal_ref:
- Phys.Rev.A71:062316,2005
- created:
- 2005-01-11
Full article ▸
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