 Since 2000 the field has seen tremendous growth. New paradigms of quantum algorithms have appeared, such as adiabatic algorithms, measurement-based algorithms, and topological-quantum-field-theory-based algorithms, as well as new physical models for realising a large scale quantum computer with cold ion traps, quantum optics (using photons and optical cavity), condensed matter systems and solid state physics (meanwhile, the first NMR model had turned out to be a dead-end with respect to scaling; see DiVincenzo (2000)). The basic questions, however, remain open even today: (1) theoretically, can quantum algorithms efficiently solve classically intractable problems? (2) operationally, can we actually realise a large scale quantum computer to run these algorithms?