Dynamics of probing a quantum-dot spin qubit with superconducting resonator photons

The hybrid system of electron spins and resonator photons is an attractive architecture for quantum computing owing to the long coherence times of spins and the promise of long-distance coupling between arbitrary pairs of qubits via photons. For the device to serve as a building block for a quantum processer, it is also necessary to readout the spin qubit state. Here we analyze in detail the measurement process of an electron spin singlet-triplet qubit in quantum dots using a coupled superconducting resonator. We show that the states of the spin singlet-triplet qubit lead to readily observable features in the spectrum of a microwave field through the resonator. These features provide useful information on the hybrid system. Moreover, we discuss the working points which can be implemented with high performance in the current state-of-the-art devices. These results can be used to construct the high fidelity measurement toolbox in the spin-circuit QED system.