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 ...

Quantum communication holds promise for absolutely secure transmission of secret messages and the faithful transfer of unknown quantum states. Photonic channels appear to be very attractive for the physical implementation of quantum communication. However, owing to losses and decoherence in the channel, the communication fidelity decreases exponentially with the channel length. Here we describe a scheme that allows the implementation of robust quantum communication over long lossy channels. The scheme involves laser manipulation of atomic ensembles, beam splitters, and single-photon detectors with moderate efficiencies, and is therefore compatible with current experimental technology. We show that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances.

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.