Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

Trap-Integrated Superconducting Nanowire Single-Photon Detectors with Improved RF Tolerance for Trapped-Ion Qubit State Readout

State readout of trapped-ion qubits with trap-integrated detectors can address important challenges for scalable quantum computing, but the strong rf electric fields used for trapping can impact detector performance. Here, we report on NbTiN superconducting nanowire single-photon detectors (SNSPDs) employing grounded aluminum mirrors as electrical shielding that are integrated into linear surface-electrode rf ion traps. The shielded SNSPDs can be operated at applied rf trapping potentials of up to 54 V_peak at 70 MHz and temperatures of up to 6 K, with a maximum system detection efficiency of 68 %. This performance should be sufficient to enable parallel high-fidelity state readout of a wide range of trapped ion species in typical cryogenic apparatus.

High-Fidelity Indirect Readout of Trapped-Ion Hyperfine Qubits

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a ^{9}Be^{+} qubit ion is mapped to a ^{25}Mg^{+} readout ion using laser-driven Raman transitions. By partitioning the ^{9}Be^{+} ground-state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of 1.2_{-0.6}^{+1.1}×10^{-4} and 0_{-0}^{+1.9}×10^{-5} with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.

Resource-Efficient Dissipative Entanglement of Two Trapped-Ion Qubits

We demonstrate a simplified method for dissipative generation of an entangled state of two trapped-ion qubits. Our implementation produces its target state faster and with higher fidelity than previous demonstrations of dissipative entanglement generation and eliminates the need for auxiliary ions. The entangled singlet state is generated in ∼7  ms with a fidelity of 0.949(4). The dominant source of infidelity is photon scattering. We discuss this error source and strategies for its mitigation.

High-fidelity laser-free universal control of trapped ion qubits

Universal control of multiple qubits-the ability to entangle qubits and to perform arbitrary individual qubit operations¹-is a fundamental resource for quantum computing², simulation³ and networking⁴. Qubits realized in trapped atomic ions have shown the highest-fidelity two-qubit entangling operations^5-7 and single-qubit rotations⁸ so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams^9-12 or by moving ions with respect to laser beams^13-15, but at lower fidelities. Laser-free entangling methods^16-20 may offer improved scalability by harnessing microwave technology developed for wireless communications, but so far their performance has lagged the best reported laser-based approaches. Here we demonstrate high-fidelity laser-free universal control of two trapped-ion qubits by creating both symmetric and antisymmetric maximally entangled states with fidelities of [Formula: see text] and [Formula: see text], respectively (68 per cent confidence level), corrected for initialization error. We use a scheme based on radiofrequency magnetic field gradients combined with microwave magnetic fields that is robust against multiple sources of decoherence and usable with essentially any trapped ion species. The scheme has the potential to perform simultaneous entangling operations on multiple pairs of ions in a large-scale trapped-ion quantum processor without increasing control signal power or complexity. Combining this technology with low-power laser light delivered via trap-integrated photonics^21,22 and trap-integrated photon detectors for qubit readout^23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.

Motional Squeezing for Trapped Ion Transport and Separation

Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.

Quantum Harmonic Oscillator Spectrum Analyzers

Characterization and suppression of noise are essential for the control of harmonic oscillators in the quantum regime. We measure the noise spectrum of a quantum harmonic oscillator from low frequency to near the oscillator resonance by sensing its response to amplitude modulated periodic drives with a qubit. Using the motion of a trapped ion, we experimentally demonstrate two different implementations with combined sensitivity to noise from 500 Hz to 600 kHz. We apply our method to measure the intrinsic noise spectrum of an ion trap potential in a previously unaccessed frequency range.

State Readout of a Trapped Ion Qubit Using a Trap-Integrated Superconducting Photon Detector

We report high-fidelity state readout of a trapped ion qubit using a trap-integrated photon detector. We determine the hyperfine qubit state of a single ^{9}Be^{+} ion held in a surface-electrode rf ion trap by counting state-dependent ion fluorescence photons with a superconducting nanowire single-photon detector fabricated into the trap structure. The average readout fidelity is 0.9991(1), with a mean readout duration of 46  μs, and is limited by the polarization impurity of the readout laser beam and by off-resonant optical pumping. Because there are no intervening optical elements between the ion and the detector, we can use the ion fluorescence as a self-calibrated photon source to determine the detector quantum efficiency and its dependence on photon incidence angle and polarization.

Frequency-comb spectroscopy on pure quantum states of a single molecular ion

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state nondestructively, leaving the molecule ready for further manipulation. We can resolve rotational transitions to 11 significant digits and derive the rotational constant of 40CaH+ to be B R = 142 501 777.9(1.7) kilohertz. Our approach is suited for a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

Quantum Logic Spectroscopy with Ions in Thermal Motion

A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions, which 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 error syndrome measurements for quantum error correction.

Quantum-enhanced sensing of a single-ion mechanical oscillator

Special quantum states are used in metrology to achieve sensitivities below the limits established by classically behaving states1,2. In bosonic interferometers, squeezed states3, number states4,5 and 'Schrödinger cat' states5 have been implemented on various platforms and have demonstrated improved measurement precision over interferometers using coherent states6,7. Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics8,9. Here we demonstrate the enhanced sensitivity of these quantum states in the case of a harmonic oscillator. We extend an existing experimental technique10 to create number states of order up to n = 100 and to generate superpositions of a harmonic oscillator ground state and a number state of the form [Formula: see text] with n up to 18 in the motion of a single trapped ion. Although experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the frequency of the mechanical oscillator. This sensitivity initially increases linearly with n and reaches a maximum at n = 12, where we observe a metrological enhancement of 6.4(4) decibels (the uncertainty is one standard deviation of the mean) compared to an ideal measurement on a coherent state with the same average occupation number. Such measurements should provide improved characterization of motional decoherence, which is an important source of error in quantum information processing with trapped ions11,12. It should also be possible to use the quantum advantage from number-state superpositions to achieve precision measurements in other harmonic oscillator systems.

Trapped-Ion Spin-Motion Coupling with Microwaves and a Near-Motional Oscillating Magnetic Field Gradient

We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.

Versatile laser-free trapped-ion entangling gates

We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a 'bichromatic' interaction picture, we show that eitherσ ^ ϕ ⊗ σ ^ ϕ orσ ^ z ⊗ σ ^ z geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. Theσ ^ z ⊗ σ ^ z gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

UV-sensitive superconducting nanowire single photon detectors for integration in an ion trap

We demonstrate superconducting nanowire single photon detectors with 76 ± 4% system detection efficiency at a wavelength of 315 nm and an operating temperature of 3.2 K, with a background count rate below 1 count per second at saturated detection efficiency. We propose integrating these detectors into planar surface electrode radio-frequency Paul traps for use in trapped ion quantum information processing. We operate detectors integrated into test ion trap structures at 3.8 K both with and without typical radio-frequency trapping electric fields. The trapping fields reduce system detection efficiency by 9%, but do not increase background count rates.

Chained Bell Inequality Experiment with High-Efficiency Measurements

We report correlation measurements on two ^{9}Be^{+} ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. A statistical framework is formulated to quantify the local-realistic fraction allowable in the observed distribution without the fair-sampling or independent-and-identical-distributions assumptions. We exclude models of our experiment whose local-realistic fraction is above 0.327 at the 95% confidence level. This bound is significantly lower than 0.586, the minimum fraction derived from a perfect Clauser-Horne-Shimony-Holt inequality experiment. Furthermore, our data provide a device-independent certification of the deterministically created Bell states.

Preparation of Entangled States through Hilbert Space Engineering

We apply laser fields to trapped atomic ions to constrain the quantum dynamics from a simultaneously applied global microwave field to an initial product state and a target entangled state. This approach comes under what has become known in the literature as "quantum Zeno dynamics" and we use it to prepare entangled states of two and three ions. With two trapped ^{9}Be^{+} ions, we obtain Bell state fidelities up to 0.990_{-5}^{+2}; with three ions, a W-state fidelity of 0.910_{-7}^{+4} is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure can be relatively insensitive to certain imperfections such as fluctuations in laser intensity.

High-Fidelity Universal Gate Set for ^{9}Be^{+} Ion Qubits

We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in ^{9}Be^{+} ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with an error per gate of 3.8(1)×10^{-5}. By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4)×10^{-4}. We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.

Arrays of individually controlled ions suitable for two-dimensional quantum simulations

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will.

Dissipative Quantum Control of a Spin Chain

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

Single-mode optical fiber for high-power, low-loss UV transmission

We report large-mode-area solid-core photonic crystal fibers made from fused silica that resist ultraviolet (UV) solarization even at relatively high optical powers. Using a process of hydrogen loading and UV irradiation of the fibers, we demonstrate stable single-mode transmission over hundreds of hours for fiber output powers of 10 mW at 280 nm and 125 mW at 313 nm (limited only by the available laser power). Fiber attenuation ranges from 0.9 dB/m to 0.13 dB/m at these wavelengths, and is unaffected by bending for radii above 50 mm.

Decoherence-assisted spectroscopy of a single Mg+ ion

We describe a high-resolution spectroscopy method in which the detection of single excitation events is enhanced by a complete loss of coherence of a superposition of two ground states. Thereby, transitions of a single isolated atom nearly at rest are recorded efficiently with high signal-to-noise ratios. Spectra display symmetric line shapes without stray-light background from spectroscopy probes. We employ this method on a (25)Mg+ ion to measure one-, two-, and three-photon transition frequencies from the 3S ground state to the 3P, 3D, and 4P excited states, respectively. Our results are relevant for astrophysics and searches for drifts of fundamental constants. Furthermore, the method can be extended to other transitions, isotopes, and species. The currently achieved fractional frequency uncertainty of 5 × 10(-9) is not limited by the method.

Micro-fabricated stylus ion trap

An electroformed, three-dimensional stylus Paul trap was designed to confine a single atomic ion for use as a sensor to probe the electric-field noise of proximate surfaces. The trap was microfabricated with the UV-LIGA technique to reduce the distance of the ion from the surface of interest. We detail the fabrication process used to produce a 150 μm tall stylus trap with feature sizes of 40 μm. We confined single, laser-cooled, (25)Mg(+) ions with lifetimes greater than 2 h above the stylus trap in an ultra-high-vacuum environment. After cooling a motional mode of the ion at 4 MHz close to its ground state (<n> = 0.34 ± 0.07), the heating rate of the trap was measured with Raman sideband spectroscopy to be 387 ± 15 quanta/s at an ion height of 62 μm above the stylus electrodes.

Demonstration of a dressed-state phase gate for trapped ions

We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.

Individual-ion addressing with microwave field gradients

Individual-qubit addressing is a prerequisite for many instances of quantum information processing. We demonstrate this capability on trapped-ion qubits with microwave near fields delivered by electrode structures integrated into a microfabricated surface-electrode trap. We describe four approaches that may be used in quantum information experiments with hyperfine levels as qubits. We implement individual control on two 25Mg+ ions separated by 4.3  μm and find spin-flip crosstalk errors on the order of 10(-3).

Sympathetic electromagnetically-induced-transparency laser cooling of motional modes in an ion chain

We use electromagnetically-induced-transparency laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply electromagnetically-induced-transparency cooling on 24Mg+ ions to cool the axial modes of a 9Be+-24Mg+ ion pair and a 9Be+-24Mg+-24Mg+-9Be+ ion chain, thereby sympathetically cooling the 9Be+ ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required laser intensity.

100-fold reduction of electric-field noise in an ion trap cleaned with in situ argon-ion-beam bombardment

Motional heating of trapped atomic ions is a major obstacle to their use as quantum bits in a scalable quantum computer. The detailed physical origin of this heating is not well understood, but experimental evidence suggests that it is caused by electric-field noise emanating from the surface of the trap electrodes. In this study, we have investigated the role of adsorbates on the electrodes by identifying contaminant overlayers, implementing an in situ argon-ion-beam cleaning treatment, and measuring ion heating rates before and after treating the trap electrodes' surfaces. We find a 100-fold reduction in heating rate after treatment. The experiments described here are sensitive to low levels of electric-field noise in the MHz frequency range. Therefore, this approach could become a useful tool in surface science that complements established techniques.

Coherent diabatic ion transport and separation in a multizone trap array

We investigate the dynamics of single and multiple ions during transport between and separation into spatially distinct locations in a multizone linear Paul trap. A single 9Be+ ion in a ~2 MHz harmonic well was transported 370 μm in 8 μs, corresponding to 16 periods of oscillation, with a gain of 0.1 motional quanta. Similar results were achieved for the transport of two ions. We also separated chains of up to 9 ions from one potential well to two distinct potential wells. With two ions this was accomplished in 55 μs, with excitations of approximately two quanta for each ion. Fast transport and separation can significantly reduce the time overhead in certain architectures for scalable quantum information processing with trapped ions.

Randomized benchmarking of multiqubit gates

We describe an extension of single-qubit gate randomized benchmarking that measures the error of multiqubit gates in a quantum information processor. This platform-independent protocol evaluates the performance of Clifford unitaries, which form a basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped ions and found an error per random two-qubit Clifford unitary of 0.162±0.008, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate inserted after each step, we extracted an error per phase gate of 0.069±0.017. We conducted these experiments with transported, sympathetically cooled ions in a multizone Paul trap-a system that can in principle be scaled to larger numbers of ions.

Efficient fiber optic detection of trapped ion fluorescence

Integration of fiber optics may play a critical role in the development of quantum information processors based on trapped ions and atoms by enabling scalable collection and delivery of light and coupling trapped ions to optical microcavities. We trap 24Mg+ ions in a surface-electrode Paul trap that includes an integrated optical fiber for detecting 280-nm fluorescence photons. The collection numerical aperture is 0.37, and total collection efficiency is 2.1%. The ion can be positioned between 80 and 100 μm from the tip of the fiber by use of an adjustable rf pseudopotential.

Quantum walk on a line for a trapped ion

We show that a multistep quantum walk can be realized for a single trapped ion with an interpolation between a quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also in its phonon number, which makes an ion-trap implementation of the quantum walk feasible.

Optimal surface-electrode trap lattices for quantum simulation with trapped ions

Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.

High-fidelity transport of trapped-ion qubits through an X-junction trap array

We report reliable transport of (9)Be(+) ions through an "X junction" in a 2D trap array that includes a separate loading and reservoir zone. During transport the ion's kinetic energy in its local well increases by only a few motional quanta and internal-state coherences are preserved. We also examine two sources of energy gain during transport: a particular radio-frequency noise heating mechanism and digital sampling noise. Such studies are important to achieve scaling in a trapped-ion quantum information processor.

Trapped-ion quantum logic gates based on oscillating magnetic fields

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit 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 current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.

Passive cooling of a micromechanical oscillator with a resonant electric circuit

We cool the fundamental mode of a miniature cantilever by capacitively coupling it to a driven rf resonant circuit. Cooling results from the rf capacitive force, which is phase shifted relative to the cantilever motion. We demonstrate the technique by cooling a 7 kHz cantilever from room temperature to 45 K, obtaining reasonable agreement with a model for the cooling, damping, and frequency shift. Extending the method to higher frequencies in a cryogenic system could enable ground state cooling and may prove simpler than related optical experiments in a low temperature apparatus.

Experimental purification of two-atom entanglement

Entanglement is a necessary resource for quantum applications--entanglement established between quantum systems at different locations enables private communication and quantum teleportation, and facilitates quantum information processing. Distributed entanglement is established by preparing an entangled pair of quantum particles in one location, and transporting one member of the pair to another location. However, decoherence during transport reduces the quality (fidelity) of the entanglement. A protocol to achieve entanglement 'purification' has been proposed to improve the fidelity after transport. This protocol uses separate quantum operations at each location and classical communication to distil high-fidelity entangled pairs from lower-fidelity pairs. Proof-of-principle experiments distilling entangled photon pairs have been carried out. However, these experiments obtained distilled pairs with a low probability of success and required destruction of the entangled pairs, rendering them unavailable for further processing. Here we report efficient and non-destructive entanglement purification with atomic quantum bits. Two noisy entangled pairs were created and distilled into one higher-fidelity pair available for further use. Success probabilities were above 35 per cent. The many applications of entanglement purification make it one of the most important techniques in quantum information processing.

Microfabricated surface-electrode ion trap for scalable quantum information processing

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.

Creation of a six-atom 'Schrödinger cat' state

Among the classes of highly entangled states of multiple quantum systems, the so-called 'Schrödinger cat' states are particularly useful. Cat states are equal superpositions of two maximally different quantum states. They are a fundamental resource in fault-tolerant quantum computing and quantum communication, where they can enable protocols such as open-destination teleportation and secret sharing. They play a role in fundamental tests of quantum mechanics and enable improved signal-to-noise ratios in interferometry. Cat states are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. Here we report the creation of cat states of up to six atomic qubits. Each qubit's state space is defined by two hyperfine ground states of a beryllium ion; the cat state corresponds to an entangled equal superposition of all the atoms in one hyperfine state and all atoms in the other hyperfine state. In our experiments, the cat states are prepared in a three-step process, irrespective of the number of entangled atoms. Together with entangled states of a different class created in Innsbruck, this work represents the current state-of-the-art for large entangled states in any qubit system.

Long-lived qubit memory using atomic ions

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

Hyperfine coherence in the presence of spontaneous photon scattering

The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.

Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

Enhanced quantum state detection efficiency through quantum information processing

We investigate theoretically and experimentally how quantum state-detection efficiency is improved by the use of quantum information processing (QIP). Experimentally, we encode the state of one 9Be(+) ion qubit with one additional ancilla qubit. By measuring both qubits, we reduce the state-detection error in the presence of noise. The deviation from the theoretically allowed reduction is due to infidelities of the QIP operations. Applying this general scheme to more ancilla qubits suggests that error in the individual qubit measurements need not be a limit to scalable quantum computation.

Realization of quantum error correction

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.