Combating dephasing decoherence by periodically performing tracking control and projective measurement

We propose a scheme to overcome phase damping decoherence by periodically performing open loop tracking control and projective measurement. Although it is impossible to stabilize a qubit subject to Markovian dynamics only by open loop coherent control, one can attain a “softened” control goal with the help of periodical projective measurement. The “softened” control objective in our scheme is to keep the state of the controlled qubit to stay near a reference pure state with a high probability for a sufficiently long time. Two suboptimal control problems are given in the sense of trace distance and fidelity, respectively, and they are eventually reduced to the design of a period T. In our scheme, one can choose the period T as long as possible if the “softened” control goal is attained. This is in contrast to the observation that quantum Zeno effect takes place only if measurements are performed in a very frequent manner, i.e., the period T must be extremely small.