Complete quantum control of a single quantum dot spin using ultrafast optical pulses

We demonstrate a complete set of ultrafast all-optical single-qubit operations on a single electron spin in a quantum dot [\textit{Nature} \textbf{456}, 218 (2008)].~ First, the spin is initialized by optical pumping into a pure spin-state with 92{\%} fidelity.~ Next, a single-qubit gate is implemented by rotating the spin about any arbitrary axis using a sequence of two ultrafast optical pulses separated by a time delay.~ Finally, the spin is measured by detecting single-photon photoluminescence.~ As a manifestation of controlling the spin with optical pulses, we demonstrate six complete Rabi oscillations between the two spin states, and a complete set of Ramsey interference fringes.~ The fidelity of our $\pi $/2- and $\pi $-rotations exceed 90{\%}.~ The single-qubit gate is completed in 38 ps, potentially allowing for approximately 10$^{5}$ operations within the qubit's expected microsecond coherence time, and quantum information processing with clock speeds exceeding 10 GHz.