  In the quantum control process, arbitrary pure or mixed initial states need
to be protected from amplitude damping through the noise channel using
measurements and quantum control. However, how to achieve it on a two-qubit
quantum system remains a challenge. In this paper, we propose a feed-forward
control approach to protect arbitrary two-qubit pure or mixed initial states
using the weak measurement. A feed-forward operation and measurements are used
before the noise channel, and afterwards a reversed operation and measurements
are applied to recover the state back to its initial state. In the case of
two-qubit pure states, we use the unravelling trick to describe the state of
the system in each step of the control procedure. For two-qubit mixed states, a
completely-positive trace-preserving (CPTP) map is implemented. Finally, the
fidelity and success probability are used to evaluate the effect of protection.
The complete recovery conditions for the measurement strengths are derived,
under which we achieve the optimal fidelity and the success probability of
recovering the initial pure or mixed states.
