Quantum computation and communication exploit the quantum properties of superposition and entanglement in order to perform tasks that may be impossible using classical means. In this Colloquium recent experimental and theoretical progress in the generation of entangled quantum networks based on the use of optical photons as carriers of information between fixed trapped atomic ion quantum memories are reviewed. Taken together, these quantum platforms offer a promising vision for the realization of a large-scale quantum network that could impact the future of communication and computation.

No abstract

Three-dimensional topological Weyl semimetals can generally support a zero-dimensional Weyl point characterized by a quantized Chern number or a one-dimensional Weyl nodal ring (or line) characterized by a quantized Berry phase in the momentum space. Here, in a dissipative system with particle gain and loss, we discover a new type of topological ring, dubbed Weyl exceptional ring consisting of exceptional points at which two eigenstates coalesce. Such a Weyl exceptional ring is characterized by both a quantized Chern number and a quantized Berry phase, which are defined via the Riemann surface. We propose an experimental scheme to realize and measure the Weyl exceptional ring in a dissipative cold atomic gas trapped in an optical lattice.Recently, condensed matter systems have proven to be a powerful platform to study low energy gapless particles by using momentum space band structures to mimic the energy-momentum relation of relativistic particles [1,2] and beyond [3][4][5][6]. One celebrated example in three dimensions is the zero-dimensional Weyl point [7][8][9][10][11][12][13][14][15][16][17][18] described by the Weyl Hamiltonian, which has been long sought-after in particle physics but only experimentally observed in condensed matter materials [19][20][21]. Such a Weyl point can be viewed as a magnetic monopole [22] in the momentum space and possesses a quantized Chern number on a surface enclosing the point. Another example is the one-dimensional Weyl nodal ring [3,[23][24][25], which has no counterpart in particle physics. It can be regarded as the generalization of zero-dimensional Dirac cones in two-dimensional systems, such as in graphene, to three-dimensional systems. Such a nodal ring has a quantized Berry phase over a closed path encircling it but does not possess a nonzero quantized Chern number. This leads to a natural question of whether there exists a topological ring exhibiting both a quantized Chern number and a quantized Berry phase in the momentum space.So far, studies on those gapless states focus on closed and lossless systems. However, particle gain and loss are generally present in natural systems. Such systems can often be described by non-Hermitian Hamiltonians [26][27][28][29], which are widely applied to many different systems [30][31][32][33][34][35][36][37][38][39][40]. Due to the non-Hermiticity, eigenvalues of the Hamiltonian are generically complex unless the PT symmetry [41] is conserved and the imaginary part of energy is associated with either decay or growth. Another intriguing feature of a non-Hermitian system is the existence of exceptional points (EPs) [26][27][28][29] at which two eigenstates coalesce and the Hamiltonian becomes defective, leading to many novel phenomena, such as lossinduced transparency [30], single-mode lasers [36,37], and reversed pump dependence of lasers [33].In this paper, we investigate a system of Weyl points in the presence of a spin-dependent non-Hermitian term and find a Weyl exceptional ring composed of EPs. In stark contrast to a Weyl nodal ...

We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A sigma_{x}sigma_{x}-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of ;{171}Yb;{+} ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.

Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.

Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses.PACS numbers: 03.67. Lx, 32.80.Qk, 03.67.Pp Trapped atomic ions remain one of the most attractive candidates for the realization of a quantum computer, owing to their long-lived internal qubit coherence and strong laser-mediated Coulomb interaction [1,2,3,4]. Various quantum gate protocols have been proposed [1,5,6,7,8,9] and many have been demonstrated with small numbers of ions [4,10,11,12,13,14]. The central challenge now is to scale up the number of trapped ion qubits to a level where the quantum behavior of the system cannot be efficiently modeled through classical means [4]. The linear rf (Paul) trap has been the workhorse for ion trap quantum computing, with atomic ions laser-cooled and confined in 1D crystals [1,2,3,4] (although there are proposals for the use of 2D crystals in a Penning trap [15] or array of microtraps [6]). However, scaling the linear ion trap to interesting numbers of ions poses significant difficulties [2,4]. As more ions are added to a harmonic axial potential, a structural instability causes the linear chain to buckle near the middle into a zigzag shape [16], and the resulting low-frequency transverse modes and the off-axis rf micromotion of the ions makes gate operation unreliable and noisy. Even in a linear chain, the complex motional mode spectrum of many ions makes it difficult to resolve individual modes for quantum gate operations, and to sufficiently laser cool many low-frequency modes. One promising approach is to operate with small linear ion chains and multiplex the system by shuttling ions between multiple chains through a maze of trapping zones, but this requires complicated electrode structures and exquisite control of ion trajectories [2,17].In this paper, we propose a new approach to ion quantum computation in a large linear architecture that circumvents the above difficulties. This scheme is based on combination of several ideas. First, an anharmonic axial trap provided by static electrode potentials can stabilize a single linear crystal containing a large number of ions. Second, tightly-confined and closely-spaced transverse phonon modes can mediate quantum gate operations in a large architecture [18], while eliminating the need for single-mode resolution and multimode sideband cooling. Third, gate operations on the large ion array exploit the local character of the laser-induced dipole interaction that is dominated by nearby ions only. As a result, the complexity of the quantum gate does not increase with the size of the system.The proposed ion architecture is illustrated in Fig. 1. It is a large linear array where the strong confi...

The authors have found typographical errors on page 2 and page 3. On page 2, Eq. (3) should readOn page 3, right-hand column, the 5th line of the second paragraph should read ''.