Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations. CONTENTS

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. This is the first time a negative Wigner function or the mutual entanglement of virtually all atoms have been attained in an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.Entanglement is now recognized as a resource for secure communication, quantum information processing, and precision measurements. An important goal is the creation of entangled states of many-particle systems while retaining the ability to characterize the quantum state and validate entanglement. Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states[1-10] have been produced in large ensembles. These states have Gaussian spin distributions and therefore can largely be modeled as systems with a classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise. Non-Gaussian states with a negative Wigner function, however, are manifestly non-classical, since the Wigner function as a quasiprobability function must remain nonnegative in the classical realm. While prior to this work a negative Wigner function had not been attained for atomic ensembles, in the optical domain, a negativevalued Wigner function has very recently been measured for states with up to 110 microwave photons [18]. Another entanglement measure is the entanglement depth [19], i.e. the minimum number of atoms that are demonstrably, but possibly weakly, entangled with one another. This paramete...

The long coherence times and strong Coulomb interactions afforded by trapped ion qubits have enabled realizations of the necessary primitives for quantum information processing (QIP) 1 , and indeed the highest-fidelity quantum operations in any qubit to date 2-4 . But while light delivery to each individual ion in a system is essential for general quantum manipulations and readout, experiments so far have employed optical systems cumbersome to scale to even a few tens of qubits 5 . Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing fully integrated within a surface-electrode ion trap chip 6 . Ion qubits are addressed at multiple locations via focusing grating couplers emitting through openings in the trap electrodes to ions trapped 50 µm above the chip; using this light we perform quantum coherent operations on the optical qubit transition in individual 88 Sr + ions. The grating focuses the beam to a diffraction-limited spot near the ion position with a 2 µm 1/e 2 -radius along the trap axis, and we measure crosstalk errors between 10 −2 and 4×10 −4 at distances 7.5-15 µm from the beam center. Owing to the scalability of the planar fabrication employed, together with the tight focusing and stable alignment afforded by optics integration within the trap chip, this approach presents a path to creating the optical systems required for large-scale trapped-ion QIP.Individual trapped ions show great promise for quantum computing; however, the lack of a scalable optical interface to manipulate and measure the quantum states of ions has been a major limitation to the development of a large-scale system 5 . Our approach to this problem utilizes nanophotonic single-mode (SM) waveguides and grating couplers integrated within the trap chip. Light is routed on chip by the waveguides and coupled by the gratings to beams with designed amplitude and phase profiles emitting from the chip towards the ions. These gratings are compact compared to the optical fibers and Fresnel lenses (both with cross-sections ≥100 µm in diameter) previously integrated with planar traps for addressing 7 and fluorescence collection 8,9 , and most importantly the planar fabrication used here to define the optics for both routing and addressing lends itself to intimate integration with the trap electrodes. Furthermore, such waveguide systems have been demonstrated to be scalable to complex geometries of thousands of devices or more 10 . Though micro-electro-mechanical systems (MEMS) mirrors integrated with traps have been proposed as well 11 , experiments so far have utilized MEMS components external to the vacuum chamber and separate from the chip 12 , leaving full integration an essential outstanding challenge.Integrated waveguide devices bring several advantages for ion addressing in planar traps. The ability to fabricate, in the same lithographically defined waveguide layer, multiple splitters, waveguide crossings, and bends with radii less than 10 µm, would enable the realization of a v...