  The theory of weak quantum measurements is developed for quantum dot spin
qubits. Building on recent experiments, we propose a control cycle to prepare,
manipulate, weakly measure, and perform quantum state tomography. This is
accomplished using a combination of the physics of electron spin resonance,
spin blockade, and Coulomb blockade, resulting in a charge transport process.
We investigate the influence of the surrounding nuclear spin environment, and
find a regime where this environment significantly simplifies the dynamics of
the weak measurement process, making this theoretical proposal realistic with
existing experimental technology. We further consider spin-echo refocusing to
combat dephasing, as well as discuss a realization of "quantum undemolition",
whereby the effects of quantum state disturbance are undone.
