Abstract

This paper presents an approach based on constructing control Hamiltonians to steer qubit states. When three tunable control Hamiltonians are available, we can adjust the controls to transform two-level quantum systems from an arbitrary initial pure state to another arbitrary target pure state along the unique geodesic curve on Block sphere. In terms of a kind of time-energy performance J = ∫ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tf</sup> [λ + (1 - λ)E(u(t))]dt, we discuss how to design control magnitude to minimize this performance. An example indicates the feasibility and efficiency of this approach on optimal control of two-level quantum systems.

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