Physics – Quantum Physics
Scientific paper
2010-09-24
J. Phys. A: Math. Theor. 44 105303 (2011)
Physics
Quantum Physics
17 pages, 1 figure, expanded version -- expanded introduction and references, added generalization of the scheme to implement
Scientific paper
10.1088/1751-8113/44/10/105303
We present a constructive control scheme for solving quantum state engineering problems based on a parametrization of the state vector in terms of complex hyperspherical coordinates. Unlike many control schemes based on factorization of unitary operators the scheme gives explicit expressions for all the Euler angles in terms of the hyperspherical coordinates of the initial and final state. The factorization, when applicable, has added benefits that phase rotations can be combined and performed concurrently. The control procedure can be realized using a simple bang-bang or square-wave-function controls. Optimal time-energy control is considered to find the optimal control amplitudes. The extension of the scheme to implement unitary operators is also discussed.
Dai Hong-Yi
Schirmer Sophie
Zhang Ming
Zhou Weiwei
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