Future technologies based on electronic spins in semiconductor quantum dots require an unprecedented level of control over the spins. Achieving this level of control is made challenging by environmental decoherence and inhomogeneous dephasing. In this talk, I will present recent progress in understanding quantitatively the primary sources of noise for spins in semiconductor nanostructures, namely the hyperfine interaction with nuclear spins and charge fluctuations. I will present new theoretical models that capture the effects of multiple noise sources on the evolution of the spin coherence and show how they can be used to develop new ways to characterize and mitigate noise. I will then describe a new general theory for combatting decoherence and inhomogeneous dephasing by driving the system in a way that such adverse effects destructively interfere and cancel out, enabling precise and robust control of a broad range of coherent quantum systems. This theory generalizes and extends existing dynamical decoupling methods, making them much more precise and versatile for ultrafast qubit manipulation.
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