English

Four-level and two-qubit systems, sub-algebras, and unitary integration

Quantum Physics 2008-11-26 v1

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)su(2)su(2) \oplus su(2) and su(2)su(2)u(1)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.

Keywords

Cite

@article{arxiv.quant-ph/0501048,
  title  = {Four-level and two-qubit systems, sub-algebras, and unitary integration},
  author = {A. R. P. Rau and G. Selvaraj and D. Uskov},
  journal= {arXiv preprint arXiv:quant-ph/0501048},
  year   = {2008}
}

Comments

1 gzip file with 1 tex and 9 eps figure files. Unpack with command: gunzip RSU05.tar.gz

R2 v1 2026-07-22T19:47:32.754Z