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arXiv · 1401.3195

Realization of quantum gates by Lyapunov control

S. C. Hou·L. C. Wang·X. X. Yi
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Abstract

We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schr\"{o}dinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in the second, the controlled-NOT (CNOT) gate is implemented in two-qubit systems with the Ising and Heisenberg interactions. Furthermore, we demonstrate that the control can drive the time-evolution operator into the local equivalence class of the CNOT gate and the operator keeps in this class forever with the existence of Ising coupling.

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S. C. Hou, L. C. Wang, X. X. Yi. 2014-01-14. Realization of quantum gates by Lyapunov control. https://doi.org/10.1016/j.physleta.2014.01.008

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