  We propose an all-electronic technique to manipulate and control interacting
quantum systems by unitary single-jump feedback conditioned on the outcome of a
capacitively coupled electrometer and in particular a single-electron
transistor. We provide a general scheme to stabilize pure states in the quantum
system and employ an effective Hamiltonian method for the quantum master
equation to elaborate on the nature of stabilizable states and the conditions
under which state purification can be achieved. The state engineering within
the quantum feedback scheme is shown to be linked with the solution of an
inverse eigenvalue problem. Two applications of the feedback scheme are
presented in detail: (i) stabilization of delocalized pure states in a single
charge qubit and (ii) entanglement stabilization in two coupled charge qubits.
In the latter example we demonstrate the stabilization of a maximally entangled
Bell state for certain detector positions and local feedback operations.
