  We investigate the optical control possibilities of spin-valley qubit carried
by single electrons localized in nanostructures of monolayer TMDs, including
small quantum dots formed by lateral heterojunction and charged impurities. The
quantum controls are discussed when the confinement induces valley
hybridization and when the valley hybridization is absent. We show that the
bulk valley and spin optical selection rules can be inherited in different
forms in the two scenarios, both of which allow the definition of spin-valley
qubit with desired optical controllability. We also investigate nuclear spin
induced decoherence and quantum control of electron-nuclear spin entanglement
via intervalley terms of the hyperfine interaction. Optically controlled
two-qubit operations in a single quantum dot are discussed.
