Quantum information science involves the storage, manipulation and communication of information encoded in quantum systems, where the phenomena of superposition and entanglement can provide enhancements over what is possible classically. Large-scale quantum information processors require stable and addressable quantum memories, usually in the form of fixed quantum bits (qubits), and a means of transferring and entangling the quantum information between memories that may be separated by macroscopic or even geographic distances. Atomic systems are excellent quantum memories, because appropriate internal electronic states can coherently store qubits over very long timescales. Photons, on the other hand, are the natural platform for the distribution of quantum information between remote qubits, given their ability to traverse large distances with little perturbation. Recently, there has been considerable progress in coupling small samples of atomic gases through photonic channels, including the entanglement between light and atoms and the observation of entanglement signatures between remotely located atomic ensembles. In contrast to atomic ensembles, single-atom quantum memories allow the implementation of conditional quantum gates through photonic channels, a key requirement for quantum computing. Along these lines, individual atoms have been coupled to photons in cavities, and trapped atoms have been linked to emitted photons in free space. Here we demonstrate the entanglement of two fixed single-atom quantum memories separated by one metre. Two remotely located trapped atomic ions each emit a single photon, and the interference and detection of these photons signals the entanglement of the atomic qubits. We characterize the entangled pair by directly measuring qubit correlations with near-perfect detection efficiency. Although this entanglement method is probabilistic, it is still in principle useful for subsequent quantum operations and scalable quantum information applications.

An outstanding goal in quantum information science is the faithful mapping of quantum information between a stable quantum memory and a reliable quantum communication channel. This would allow, for example, quantum communication over remote distances, quantum teleportation of matter and distributed quantum computing over a 'quantum internet'. Because quantum states cannot in general be copied, quantum information can only be distributed in these and other applications by entangling the quantum memory with the communication channel. Here we report quantum entanglement between an ideal quantum memory--represented by a single trapped 111Cd+ ion--and an ideal quantum communication channel, provided by a single photon that is emitted spontaneously from the ion. Appropriate coincidence measurements between the quantum states of the photon polarization and the trapped ion memory are used to verify their entanglement directly. Our direct observation of entanglement between stationary and 'flying' qubits is accomplished without using cavity quantum electrodynamic techniques or prepared non-classical light sources. We envision that this source of entanglement may be used for a variety of quantum communication protocols and for seeding large-scale entangled states of trapped ion qubits for scalable quantum computing.

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171 Yb + , with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

We observe violation of a Bell inequality between the quantum states of two remote Yb+ ions separated by a distance of about 1 m with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint detection of two emitted photons, whose polarization is entangled with each ion. The entanglement of remote qubits is also characterized by full quantum state tomography.

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

Trapped atomic ions are among the most attractive implementations of quantum bits for applications in quantuminformation processing, owing to their long trapping lifetimes and long coherence times. Although nearby trapped ions can be entangled through their Coulomb-coupled motion 1-6 , it seems more natural to entangle remotely located ions through a coupling mediated by photons, eliminating the need to control the ion motion. A promising way to entangle ions via a photonic channel is to interfere two photons emitted from the ions and then detect appropriate photon coincidence events 7-9 . Here, we report the pivotal element of this scheme in the observation of quantum interference between pairs of single photons emitted from two atomic ions residing in independent traps.Remote entanglement of two ions or atoms can be achieved by subjecting two photons emitted by the particles to a Bellstate measurement and is heralded by an appropriate coincidence detection of the photons 7 . The essence of this Bell-state measurement is the quantum interference of two photons, which has been observed previously with photons generated in a variety of physical processes and systems, including nonlinear optical down-conversion 10,11 , quantum dots 12 , atoms in cavity quantum electrodynamics 13 , atomic ensembles 14-16 and two nearby trapped neutral atoms 17 . We report the first observation of interference between two single photons emitted from two remote trapped atomic ions. The two Yb ions are stored in independent traps in two vacuum chambers separated by about one metre. The interference of two single photons emitted by remote ions is the only element of remote-entanglement schemes that has not previously been demonstrated. Hence, this demonstration is an essential step towards future remote-ion-entanglement experiments, which may ultimately lead to large-scale quantum networks [18][19][20][21][22][23] . In the experiment, single 174 Yb + ions are trapped in two congeneric Paul traps located in separate vacuum chambers as described in detail in the Methods section. Laser cooling localizes the ions to within the resolution of the diffraction-limited imaging optics but well outside the Lamb-Dicke limit. The ions are excited with ultrafast laser pulses generated by a picosecond mode-locked Ti:sapphire laser with a centre frequency of 739 nm. Each pulse is then frequency doubled to 369.5 nm through a phase-matched lithium triborate nonlinear crystal. An electro-optic pulse picker is used to reduce the pulse repetition rate from 81 MHz to 8.1 MHz with an extinction ratio of better than 10 4 :1. The second harmonic is filtered from the fundamental with a prism, split between the two traps using a beam splitter and aligned to arrive at the two ions within 100 ps of each other. Each pulse has a neartransform-limited pulse duration of 2 ps and excites the ions on a timescale much faster than the excited-state lifetime of 8 ns. The 174 Yb + ion is collected using a triplet lens with a numerical aperture of 0.23 and a working distanc...

We present the design, fabrication, and experimental implementation of surface ion traps with Y-shaped junctions. The traps are designed to minimize the pseudopotential variations in the junction region at the symmetric intersection of three linear segments. We experimentally demonstrate robust linear and junction shuttling with greater than 10 6 round-trip shuttles without ion loss. By minimizing the direct line of sight between trapped ions and dielectric surfaces, negligible day-to-day and trap-to-trap variations are observed. In addition to high-fidelity single-ion shuttling, multiple-ion chains survive splitting, ion-position swapping, and recombining routines. The development of two-dimensional trapping structures is an important milestone for ion-trap quantum computing and quantum simulations. arXiv:1105.1834v1 [quant-ph]

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