We demonstrated coherent control of a quantum two-level system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. These techniques are based on rapid electrical control of the exchange interaction. Separating and later recombining a singlet spin state provided a measurement of the spin dephasing time, T 2 *, of È10 nanoseconds, limited by hyperfine interactions with the gallium arsenide host nuclei. Rabi oscillations of two-electron spin states were demonstrated, and spin-echo pulse sequences were used to suppress hyperfine-induced dephasing. Using these quantum control techniques, a coherence time for two-electron spin states exceeding 1 microsecond was observed.Quantum coherence and entanglement have emerged as physical bases for informationprocessing schemes that use two-state quantum systems (quantum bits or qubits) to provide efficient computation and secure communication (1, 2). Although quantum control of entanglement has been realized in isolated atomic systems, its extension to solid-state systemsmotivated by the prospect of scalable device fabrication-remains a demanding experimental goal (3, 4), particularly because of the stronger coupling of solid-state qubits to their environment. Understanding this coupling and learning how to control quantum systems in the solid state is a major challenge of modern condensed-matter physics (5, 6).An attractive candidate for a solid-state qubit is based on semiconductor quantum dots, which allow controlled coupling of one or more electrons, using rapidly switchable voltages applied to electrostatic gates (7-9). Recent experiments suggest that spin in quantum dots may be a particularly promising holder of quantum information, because the spin relaxation time (T 1 ) can approach tens of milliseconds (10-13). Although gallium arsenide (GaAs) is a demonstrated exceptional material for fabricating quantum dots, it has the potential drawback that confined electrons interact with on the order of 10 6 spin-3/2 nuclei through the hyperfine interaction. Here we present a quantum two-level system (logical qubit) based on two-electron spin states (14) and demonstrate coherent control of this system through the use of fast electrical control of the exchange interaction. We first show by direct time-domain measurements that the time-ensemble-averaged dephasing time (T 2 *) of this qubit is È10 ns, limited by hyperfine interactions. We then demonstrate Rabi oscillations in the two-spin space (including a 180-ps ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi SWAP p operation between two electron spins) and implement spin-echo sequences, showing an extended spin coherence time, T 2 , beyond 1 ms.Isolating and measuring two electrons. Gate-defined double quantum dot devices are fabricated using a GaAs/AlGaAs heterostructure grown by molecular beam epitaxy with a two-dimensional electron gas 100 nm below the surface, with density È2 Â 10 11 cm j2 . When biased with negative voltages, the patterned gates ...

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.

We manipulate a single electron in a fully tunable double quantum dot using microwave excitation. Under resonant conditions, microwaves drive transitions between the (1,0) and (0,1) charge states of the double dot. Local quantum point contact charge detectors enable a direct measurement of the photon-induced change in occupancy of the charge states. From charge sensing measurements, we find T1 approximately 16 ns and a lower bound estimate for T*(2) of 400 ps for the charge two-level system.