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Trapped atomic ions are natural candidates for quantum information processing and have the potential to realize or improve quantum computing, sensing, and networking. These applications often require the collection of individual photons emitted from ions into guided optical modes, in some cases for the production of entanglement between separated ions. Proof-of-principle demonstrations of such photon collection from trapped ions have been performed using high-numerical-aperture lenses or cavities and single-mode fibers, but integrated photonic elements in ion-trap structures offer advantages in scalability and manufacturabilty over traditional optics. In this paper we analyze structures monolithically fabricated with an ion trap for collecting ion-emitted photons, coupling them into waveguides, and manipulating them via interference. We calculate geometric limitations on collection efficiency for this scheme, simulate a single-layer grating that shows performance comparable to demonstrated free-space optics, and discuss practical fabrication and fidelity considerations. Based on this analysis, we conclude that integrated photonics can support scalable systems of trapped-ions that can distribute quantum information via photon-mediated entanglement., Comment: 25 pages, 6 figures, 2 tables. File updated to version published in Optica Quantum

Quantum Signal Processing (QSP) has emerged as a promising framework to manipulate and determine properties of quantum systems. QSP not only unifies most existing quantum algorithms but also provides tools to discover new ones. Quantum signal processing is applicable to single- or multi-qubit systems that can be qubitized so one can exploit the SU$(2)$ structure of system evolution within special invariant two-dimensional subspaces. In the context of quantum algorithms, this SU$(2)$ structure is artificially imposed on the system through highly nonlocal evolution operators that are difficult to implement on near-term quantum devices. In this work, we propose QSP protocols for the infinite-dimensional Onsager Lie Algebra, which is relevant to the physical dynamics of quantum devices that can simulate the transverse field Ising model. To this end, we consider QSP sequences in the Heisenberg picture, allowing us to exploit the emergent SU$(2)$ structure in momentum space and synthesize QSP sequences for the Onsager algebra. Our results demonstrate a concrete connection between QSP techniques and Noisy Intermediate Scale quantum protocols. We provide examples and applications of our approach in diverse fields ranging from space-time dual quantum circuits and quantum simulation, to quantum control., Comment: 14 pages, 4 figures. Comments are welcome

Trapped-ion quantum information processing may benefit from qubits encoded in isotopes that are practically available in only small quantities, e.g. due to low natural abundance or radioactivity. Laser ablation provides a method of controllably liberating neutral atoms or ions from low-volume targets, but energetic ablation products can be difficult to confine in the small ion-electrode distance, micron-scale, microfabricated traps amenable to high-speed, high-fidelity manipulation of ion arrays. Here we investigate ablation-based ion loading into surface-electrode traps of different sizes to test a model describing ion loading probability as a function of effective trap volume and other trap parameters. We demonstrate loading of ablated and photoionized barium in two cryogenic surface-electrode traps with 730 $\mu$m and 50 $\mu$m ion-electrode distances. Our loading success probability agrees with a predictive analytical model, providing insight for the confinement of limited-quantity species of interest for quantum computing, simulation, and sensing.

Quantum computers, much like their classical counterparts, will likely benefit from flexible qubit encodings that can be matched to different tasks. For trapped ion quantum processors, a common way to access multiple encodings is to use multiple, co-trapped atomic species. Here, we outline an alternative approach that allows flexible encoding capabilities in single-species systems through the use of long-lived metastable states as an effective, programmable second species. We describe the set of additional trapped ion primitives needed to enable this protocol and show that they are compatible with large-scale systems that are already in operation.

Trapped-ion quantum information processors offer many advantages for achieving high-fidelity operations on a large number of qubits, but current experiments require bulky external equipment for classical and quantum control of many ions. We demonstrate the cryogenic operation of an ion-trap that incorporates monolithically-integrated high-voltage CMOS electronics ($\pm 8\mathrm{V}$ full swing) to generate surface-electrode control potentials without the need for external, analog voltage sources. A serial bus programs an array of 16 digital-to-analog converters (DACs) within a single chip that apply voltages to segmented electrodes on the chip to control ion motion. Additionally, we present the incorporation of an integrated circuit that uses an analog switch to reduce voltage noise on trap electrodes due to the integrated amplifiers by over $50\mathrm{dB}$. We verify the function of our integrated electronics by performing diagnostics with trapped ions and find noise and speed performance similar to those we observe using external control elements., Comment: 7 pages, 3 figures

We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This is the first demonstration of scalable quantum computing hardware, in any modality, utilizing a commercial CMOS process, and it opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays., Comment: 4 pages, 3 figures

A general method for rotational microwave spectroscopy and control of polar molecular ions via direct microwave addressing is considered. Our method makes use of spatially varying AC Stark shifts, induced by far off-resonant, focused laser beams to achieve an effective coupling between the rotational state of a molecular ion and the electronic state of an atomic ion. In this setting, the atomic ion is used for read-out of the molecular ion state, in a manner analogous to quantum logic spectroscopy based on Raman transitions. In addition to high-precision spectroscopy, this setting allows for rotational ground state cooling, and can be considered as a candidate for the quantum information processing with polar molecular ions. All elements of our proposal can be realized with currently available technology.

A new approach for realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed., Comment: 4 pages, 2 figures, minor improvements, published in Physical Review Letters

A scalable, multiplexed ion trap for quantum information processing is fabricated and tested. The trap design and fabrication process are optimized for scalability to small trap size and large numbers of interconnected traps, and for integration of control electronics and optics. Multiple traps with similar designs are tested with Cd+, Mg+, and Sr+ ions at room temperature and with Sr+ at 6 K, with respective ion lifetimes of 90 s, 300 +/- 30 s, 56 +/- 6 s, and 4.5 +/- 1.1 hours. The motional heating rate for Mg+ at room temperature and a trap frequency of 1.6 MHz is measured to be 7 +/- 3 quanta per millisecond. For Sr+ at 6 K and 540 kHz the heating rate is measured to be 220 +/- 30 quanta per second., Comment: 18 pages, 12 figures

We propose an approach for studying quantum information and performing high resolution spectroscopy of rotational states of trapped molecular ions using an on-chip superconducting microwave resonator. Molecular ions have several advantages over neutral molecules. Ions can be loaded into deep (1 eV) RF traps and are trapped independent of the electric dipole moment of their rotational transition. Their charge protects them from motional dephasing and prevents collisional loss, allowing 1 s coherence times when used as a quantum memory, with detection of single molecules possible in <10 ms. An analysis of the detection efficiency and coherence properties of the molecules is presented., Comment: 9 pages, 1 figure

We present two simple cryogenic RF ion trap systems in which cryogenic temperatures and ultra high vacuum pressures can be reached in as little as 12 hours. The ion traps are operated either in a liquid helium bath cryostat or in a low vibration closed cycle cryostat. The fast turn around time and availability of buffer gas cooling made the systems ideal for testing surface-electrode ion traps. The vibration amplitude of the closed cycled cryostat was found to be below 106 nm. We evaluated the systems by loading surface-electrode ion traps with $^{88}$Sr$^+$ ions using laser ablation, which is compatible with the cryogenic environment. Using Doppler cooling we observed small ion crystals in which optically resolved ions have a trapped lifetime over 2500 minutes., Comment: 10 pages, 13 EPS figures

Chiaverini et al. [Quant. Inf. Comput. 5, 419 (2005)] recently suggested a linear Paul trap geometry for ion trap quantum computation that places all of the electrodes in a plane. Such planar ion traps are compatible with modern semiconductor fabrication techniques and can be scaled to make compact, many zone traps. In this paper we present an experimental realization of planar ion traps using electrodes on a printed circuit board to trap linear chains of tens of 0.44 micron diameter charged particles in a vacuum of 15 Pa (0.1 torr). With these traps we address concerns about the low trap depth of planar ion traps and develop control electrode layouts for moving ions between trap zones without facing some of the technical difficulties involved in an atomic ion trap experiment. Specifically, we use a trap with 36 zones (77 electrodes) arranged in a cross to demonstrate loading from a traditional four rod linear Paul trap, linear ion movement, splitting and joining of ion chains, and movement of ions through intersections. We further propose an additional DC biased electrode above the trap which increases the trap depth dramatically, and a novel planar ion trap geometry that generates a two dimensional lattice of point Paul traps., Comment: 11 pages, 20 figures

An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent estimates of the threshold are near some experimentally achieved gate fidelities. However, the landscape of threshold estimates includes pseudothresholds, threshold estimates based on a subset of components and a low level of recursion. In this paper, we observe that pseudothresholds are a generic phenomenon in fault-tolerant computation. We define pseudothresholds and present classical and quantum fault-tolerant circuits exhibiting pseudothresholds that differ by a factor of 4 from fault-tolerance thresholds for typical relationships between component failure rates. We develop tools for visualizing how reliability is influenced by recursive simulation in order to determine the asymptotic threshold. Finally, we conjecture that refinements of these methods may establish upper bounds on the fault-tolerance threshold for particular codes and noise models., Comment: 20 pages, 16 figures, to appear in QIC

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to an RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin., Comment: 5 pages, 4 figures

We present gate-dependent transport measurements of Kondo impurities in bare gold break junctions, generated with high yield using an electromigration process that is actively controlled. Thirty percent of measured devices show zero-bias conductance peaks. Temperature dependence suggests Kondo temperatures \~7K. The peak splitting in magnetic field is consistent with theoretical predictions for g=2, though in many devices the splitting is offset from 2guB by a fixed energy. The Kondo resonances observed here may be due to atomic-scale metallic grains formed during electromigration., Comment: 5 pages, 3 figures

When a quantum system interacts with an external environment, it undergoes the loss of quantum correlation (decoherence) and the loss of energy (relaxation) and eventually all of the quantum information becomes classical. Here we show a general principle to use unitary operations to establish and preserve particular non-equilibrium states in arbitrary relaxing quantum systems. We elucidate these concepts with examples of state preservation in one-spin and two-spin entangled systems., Comment: 4 pages, 2 figures, RevTex4

Decoherence in quantum computers is formulated within the Semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for error-less quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators. It is shown that these subspaces are stable to perturbations and moreover, that universal quantum computation is possible within them., Comment: 4 pages, no figures. Conditions for decoherence-free subspaces made more explicit, updated references. To appear in PRL

We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single-qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels., Comment: 4 pages Revtex + 1 fig, pictures at http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small corrections

We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification., Comment: 7 pages, 2 figures, submitted to Phys. Rev. A

Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant error process in a physical system is often well known, thus inviting the question: given a specific error model, can more efficient codes be devised? We demonstrate new codes which correct just amplitude damping errors which allow, for example, a t=1, k=1 code using effectively n=4.6. Our scheme is based on using bosonic states of photons in a finite number of optical modes. We present necessary and sufficient conditions for the codes, and describe construction algorithms, physical implementation, and performance bounds., Comment: 12 pages, 3 figures, psfig, revtex, submitted to Phys. Rev. A