Weak measurement of quantum dot spin qubits

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.