Practical and useful quantum information processing (QIP) requires significant improvements with respect to current systems, both in error rates of basic operations and in scale. Individual trapped-ion qubits' fundamental qualities are promising for long-term systems, but the optics involved in their precise control are a barrier to scaling. Planar-fabricated optics integrated within ion trap devices can make such systems simultaneously more robust and parallelizable, as suggested by previous work with single ions. Here we use scalable optics co-fabricated with a surface-electrode ion trap to achieve high-fidelity multi-ion quantum logic gates, often the limiting elements in building up the precise, large-scale entanglement essential to quantum computation. Light is efficiently delivered to a trap chip in a cryogenic environment via direct fibre coupling on multiple channels, eliminating the need for beam alignment into vacuum systems and cryostats and lending robustness to vibrations and beam pointing drifts. This allows us to perform ground-state laser cooling of ion motion, and to implement gates generating two-ion entangled states with fidelities $>99.3(2)\%$. This work demonstrates hardware that reduces noise and drifts in sensitive quantum logic, and simultaneously offers a route to practical parallelization for high-fidelity quantum processors. Similar devices may also find applications in neutral atom and ion-based quantum-sensing and timekeeping.
We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser field…
We demonstrate parallel composite quantum logic gates with phases implemented locally through nanoscale movement of ions within a global laser beam of fixed pulse duration. We show that a simple four-pulse sequence suffices for constructing ideal arbitrary single-qubit rotations in the presence of large intensity inhomogeneities across the ion trap due to laser beam-pointing or beam-focusing. Using such sequences, we perform parallel arbitrary rotations on ions in two trapping zones separated by 700 $μ$m with fidelities comparable to those of our standard laser-controlled gates. Our scheme imp…
We demonstrate the excitation of ions to the Rydberg state $22F$ by vacuum ultraviolet radiation at a wavelength of $123\,\text{nm}$ combined with the coherent manipulation of the optical qubit transition in $^{40}\text{Ca}^+$. With a tightly focused beam at $729\,\text{nm}$ wavelength we coherently excite a single ion from a linear string into the metastable $3D_{5/2}$ state before a VUV pulse excites it to the Rydberg state. In combination with ion shuttling in the trap, we extend this approach to the addressed excitation of multiple ions. The coherent initialization as well as the addressed…
We present a quantum logic scheme to detect atomic and molecular ions in different states of angular momentum based on their magnetic $g$-factors. The state-dependent magnetic $g$-factors mean that electronic, rotational or hyperfine states may be distinguished by their Zeeman splittings in a given magnetic field. Driving motional sidebands of a chosen Zeeman splitting enables reading out the corresponding state of angular momentum with an auxillary logic ion. As a proof-of-principle demonstration, we show that we can detect the ground electronic state of a ${^{174}}$Yb$^+$ ion using ${^{171}}…
A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions that combines probe and information transfer from the spectroscopy to the logic ion in a single pulse. We experimentally realize this method, show how it can be applied as a technique for identifying transitions in currently intractable atoms or molecules, demonstrate its reduced temperature sensitivity, and observe quantum-enhanced frequency sensitivity when it is applied to multi-ion chains. Potential applications include improved readout of trapped-ion clocks and simplified err…
We present a multilayer surface-electrode ion trap with embedded 3D microwave circuitry for implementing entangling quantum logic gates. We discuss the electromagnetic full-wave simulation procedure that has led to the trap design and the characterization of the resulting microwave field-pattern using a single ion as a local field probe. The results agree with simulations within the uncertainty; compared to previous traps, this design reduces detrimental AC Zeeman shifts by three orders of magnitude. The design presented here can be viewed as an entangling gate component in a library for surfa…
Fluorescence collection sets the efficiency of state detection and the rate of entanglement generation between remote trapped ion qubits. Despite efforts to improve light collection using various optical elements, solid angle capture is limited to ~10% for implementations that are scalable to many ions. We present an approach based on fluorescence detection through a transparent trap using an integrated photodetector, combining collection efficiency approaching 50% with scalability. We microfabricate transparent surface traps with indium tin oxide and verify stable trapping of single ions. The…
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that vir…
We use a co-trapped ion ($^{88}\mathrm{Sr}^{+}$) to sympathetically cool and measure the quantum state populations of a memory-qubit ion of a different atomic species ($^{40}\mathrm{Ca}^{+}$) in a cryogenic, surface-electrode ion trap. Due in part to the low motional heating rate demonstrated here, the state populations of the memory ion can be transferred to the auxiliary ion by using the shared motion as a quantum state bus and measured with an average accuracy of 96(1)%. This scheme can be used in quantum information processors to reduce photon-scattering-induced error in unmeasured memory …
One limit to the fidelity of quantum logic operations on trapped ions arises from heating of the ions' collective modes of motion. Sympathetic cooling of the ions during the logic operations may eliminate this source of errors. We discuss benefits and drawbacks of this proposal, and describe possible experimental implementations. We also present an overview of trapped-ion dynamics in this scheme.
Trapped ions are promising candidates for nodes of a scalable quantum network due to their long-lived qubit coherence times and high-fidelity single and two-qubit gates. Future quantum networks based on trapped ions will require a scalable way to route photons between different nodes. Photonic integrated circuits from fabrication foundries provide a compact solution to this problem. However, these circuits typically operate at telecommunication wavelengths which are incompatible with the strong dipole emissions of trapped ions. In this work, we demonstrate the routing of single photons from a …
In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of $^{25}\text{Mg}^+$ logic ions and $^{27}\text{Al}^+$ spectroscopy ions. We observe…
We propose a scheme for implementation of logical gates in a trapped ion inside a high-Q cavity. The ion is simultaneously interacting with a (classical) laser field as well as with the (quantized) cavity field. We demonstrate that simply by tuning the ionic internal levels with the frequencies of the fields, it is possible to construct a controlled-NOT gate in a three step procedure, having the ion's internal as well as motional levels as qubits. The cavity field is used as an auxiliary qubit and basically remains in the vacuum state.
We demonstrate key multi-qubit quantum logic primitives in a dual-species trapped-ion system based on $^{40}$Ca+ and $^{88}$Sr+ ions, using two optical qubits with quantum-logic-control frequencies in the red to near-infrared range. With all ionization, cooling, and control wavelengths in a wavelength band similar for the two species and centered in the visible, and with a favorable mass ratio for sympathetic cooling, this pair is a promising candidate for scalable quantum information processing. Same-species and dual-species two-qubit gates, based on the Moelmer-Soerensen interaction and perf…
JILA, National Institute of Standards and Technology, University of Colorado（科罗拉多大学国家物理测量局联合研究所）；Department of Physics, University of Colorado（科罗拉多大学物理系）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学霍默·L·道奇物理与天文学系）；Center for Quantum Research and Technology, The University of Oklahoma（俄克拉荷马大学量子研究与技术中心）；Time and Frequency Division, National Institute of Standards and Technology（国家物理测量局时间与频率司）；Center for Theory of Quantum Matter, University of Colorado（科罗拉多大学量子物质理论中心）
Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmic…
We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.
Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO$^+$, and discuss progress towards experimental realization…
Monolithic integration of control technologies for atomic systems is a promising route to the development of quantum computers and portable quantum sensors. Trapped atomic ions form the basis of high-fidelity quantum information processors and high-accuracy optical clocks. However, current implementations rely on free-space optics for ion control, which limits their portability and scalability. Here we demonstrate a surface-electrode ion-trap chip using integrated waveguides and grating couplers, which delivers all the wavelengths of light required for ionization, cooling, coherent operations,…
We present a novel, single-ion trap with integrated optical fibers directly embedded within the trap structure to deliver laser light as well as collect the ion's fluorescence. This eliminates the need for optical windows. We characterise the system's performance and measure signal-to-background ratios in the ion's fluorescence on the order of 50, which allows us to perform state readout with a fidelity over 99% in 600 $μ$s. We test the system's resilience to thermal variations in the range between 22°C and 53°C, and the system's vibration resilience at 34 Hz and 300 Hz and find no effect on i…
Integrated technologies greatly enhance the prospects for practical quantum information processing and sensing devices based on trapped ions. High-speed and high-fidelity ion state readout is critical for any such application. Integrated detectors offer significant advantages for system portability and can also greatly facilitate parallel operations if a separate detector can be incorporated at each ion-trapping location. Here we demonstrate ion quantum state detection at room temperature utilizing single-photon avalanche diodes (SPADs) integrated directly into the substrate of silicon ion tra…
We consider the feasibility of performing quantum logic operations based on stimulated Raman transitions in trapped Calcium ions. This technique avoids many of the technical difficulties involved with laser stabilisation, and only three laser wavelengths are required, none of which need have particularly stringent requirements on their bandwidths. The possible problems with experimental realisations are discussed in detail.
We present a scheme utilizing position-dependent ac Stark shifts for doing quantum logic with trapped ions. By a proper choice of direction, position and size, as well as power and frequency of a far-off-resonant Gaussian laser beam, specific ac Stark shifts can be assigned to the individual ions, making them distinguishable in frequency-space. In contrast to previous all-optical based quantum gates with trapped ions, the present scheme enables individual addressing of single ions and selective addressing of any pair of ions for two-ion quantum gates, without using tightly focused laser beams.…
Essentially all known quantum gates rely on a weak-coupling approximation resulting in linear dynamics. With the explicit example of trapped ions, we show how high-fidelity quantum gates can be achieved outside such an approximation, and we derive readily implementable driving fields to realize gates with extremely high fidelities for ions well outside the Lamb-Dicke regime with motional temperatures achievable by only Doppler cooling.
Quantum bits based on individual trapped atomic ions constitute a promising technology for building a quantum computer, with all the elementary operations having been achieved with the necessary precision for some error-correction schemes. However, the essential two-qubit logic gate used for generating quantum entanglement has hitherto always been performed in an adiabatic regime, where the gate is slow compared with the characteristic motional frequencies of ions in the trap, giving logic speeds of order 10kHz. There have been numerous proposals for performing gates faster than this natural "…
We simulate four quantum error correcting codes under error models inspired by realistic noise sources in near-term ion trap quantum computers: $T_2$ dephasing, gate overrotation, and crosstalk. We use this data to find preferred codes for given error parameters along with logical error biases and a pseudothreshold which compares the physical and logical gate failure rates for a CNOT gate. Using these results we conclude that Bacon-Shor-13 is the most promising near term candidate as long as the impact of crosstalk can be mitigated through other means.
A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency …
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), and indeed the highest-fidelity quantum operations in any qubit to date. 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. Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing fully integ…
A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $η_{L}=η_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.
We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $\sim0.1\%$ level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between $97.1(2)\%$ (for a gate time $t_g=3.8μ$s) and $99.9(1)\%$ (for $t_g=100μ$s), representing respectively the fastest and lowest-error two-qubit…
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 …
Quantum networking links quantum processors through remote entanglement for distributed quantum information processing (QIP) and secure long-range communication. Trapped ions are a leading QIP platform, having demonstrated universal small-scale processors and roadmaps for large-scale implementation. Overall rates of ion-photon entanglement generation, essential for remote trapped ion entanglement, are limited by coupling efficiency into single mode fibres5 and scaling to many ions. Here we show a microfabricated trap with integrated diffractive mirrors that couples 4.1(6)% of the fluorescence …
We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential. We aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors for different mirror orientations with respect to the trapping electrodes, as well as for mirror misalignment. We also analyze…
One of the outstanding challenges for ion trap quantum information processing is to accurately detect the states of many ions in a scalable fashion. In the particular case of surface traps, geometric constraints make imaging perpendicular to the surface appealing for light collection at multiple locations with minimal cross-talk. In this report we describe an experiment integrating Diffractive Optic Elements (DOE's) with surface electrode traps, connected through in-vacuum multi-mode fibers. The square DOE's reported here were all designed with solid angle collection efficiencies of 3.58%; wit…
In this article we describe the design, construction and implementation of our ion-atom hybrid system incorporating a high resolution time of flight mass spectrometer (TOFMS). Potassium atoms ($^{39}$K) in a Magneto Optical Trap (MOT) and laser cooled calcium ions ($^{40}$Ca$^+$) in a linear Paul trap are spatially overlapped and the combined trap is integrated with a TOFMS for radial extraction and detection of reaction products. We also present some experimental results showing interactions between $^{39}$K$^+$ and $^{39}$K, $^{40}$Ca$^+$ and $^{39}$K$^+$ as well as $^{40}$Ca$^+$ and $^{39}$…
Due to their rich level structure, molecules are well-suited for probing time variation of fundamental constants, precisely measuring parity violation and time-reversal non-invariance effects, studying quantum mechanical aspects of chemical reactions, and implementing scalable quantum information processing architectures. Molecular ions are particularly attractive for these applications due to their long storage times and the near-perfect isolation from environment that result in long coherence times required to achieve high measurement precision and reduce systematic errors. However, the cont…
We present the design, fabrication, and characterization of a segmented surface ion trap with integrated current carrying structures. The latter produce a spatially varying magnetic field necessary for magnetic gradient induced coupling between ionic effective spins. We demonstrate trapping of strings of 172Yb+ ions, characterize the performance of the trap and map magnetic fields by radio frequency-optical double resonance spectroscopy. In addition, we apply and characterize the magnetic gradient and demonstrate individual addressing in a string of three ions using RF radiation.
Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating ions (quantum memory) with photons (distance link) offers a unique path to large-scale quantum computation and long-distance quantum communication. In this article, we present a detailed review of the experimental implementation of a heralded photon-mediated quantum gate between remote ions, and the employment of this gate to perform a teleportation…
We propose the implementation of selective interactions of atom-motion subspaces in trapped ions. These interactions yield resonant exchange of population inside a selected subspace, leaving the others in a highly dispersive regime. Selectivity allows us to generate motional Fock (and other nonclassical) states with high purity out of a wide class of initial states, and becomes an unconventional cooling mechanism when the ground state is chosen. Individual population of number states can be distinctively measured, as well as the motional Wigner function. Furthermore, a protocol for implementin…
We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field.
In this study, we report the first Cu-filled through silicon via (TSV) integrated ion trap. TSVs are placed directly underneath electrodes as vertical interconnections between ion trap and a glass interposer, facilitating the arbitrary geometry design with increasing electrodes numbers and evolving complexity. The integration of TSVs reduces the form factor of ion trap by more than 80%, minimizing parasitic capacitance from 32 to 3 pF. A low RF dissipation is achieved in spite of the absence of ground screening layer. The entire fabrication process is on 12-inch wafer and compatible with estab…
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multi-qubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser beam control and motional state initialization compared to c…
We introduce a novel scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac-Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit…
An atomic ion is trapped at the tip of a single-mode optical fiber in a cryogenic (8 K) surface-electrode ion trap. The fiber serves as an integrated source of laser light, which drives the quadrupole qubit transition of $^{88}$Sr$^+$. Through \emph{in situ} translation of the nodal point of the trapping field, the Gaussian beam profile of the fiber output is imaged, and the fiber-ion displacement, in units of the mode waist at the ion, is optimized to within $0.13\pm0.10$ of the mode center despite an initial offset of $3.30\pm0.10$. Fiber-induced charging at $125 μ$W is observed to be ${\sim…
