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

Material-Inherent Noise Sources in Quantum Information Architecture

NISQ is a representative keyword at present as an acronym for "noisy intermediate-scale quantum", which identifies the current era of quantum information processing (QIP) technologies. QIP science and technologies aim to accomplish unprecedented performance in computation, communications, simulations, and sensing by exploiting the infinite capacity of parallelism, coherence, and entanglement as governing quantum mechanical principles. For the last several decades, quantum computing has reached to the technology readiness level 5, where components are integrated to build mid-sized commercial products. While this is a celebrated and triumphant achievement, we are still a great distance away from quantum-superior, fault-tolerant architecture. To reach this goal, we need to harness technologies that recognize undesirable factors to lower fidelity and induce errors from various sources of noise with controllable correction capabilities. This review surveys noisy processes arising from materials upon which several quantum architectures have been constructed, and it summarizes leading research activities in searching for origins of noise and noise reduction methods to build advanced, large-scale quantum technologies in the near future.

Fast and high-yield fabrication of axially symmetric ion-trap needle electrodes via two step electrochemical etching

Despite the progress in building sophisticated microfabricated ion traps, Paul traps employing needle electrodes retain their significance due to the simplicity of fabrication while producing high-quality systems suitable for quantum information processing, atomic clocks, etc. For low noise operations such as minimizing "excess micromotion," needles should be geometrically straight and aligned precisely with respect to each other. Self-terminated electrochemical etching, previously employed for fabricating ion-trap needle electrodes, employs a sensitive and time-consuming technique, resulting in a low success rate of usable electrodes. Here, we demonstrate an etching technique for the quick fabrication of straight and symmetric needles with a high success rate and a simple apparatus with reduced sensitivity to alignment imperfections. The novelty of our technique comes from using a two-step approach employing turbulent etching for fast shaping and slow etching/polishing for subsequent surface finish and tip cleaning. Using this technique, needle electrodes for an ion trap can be fabricated within a day, significantly reducing the setup time for a new apparatus. The needles fabricated via this technique have been used in our ion trap to achieve trapping lifetimes of several months.

High-Fidelity Ion State Detection Using Trap-Integrated Avalanche Photodiodes

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 trapping chips. We detect the state of a trapped Sr^{+} ion via fluorescence collection with the SPAD, achieving 99.92(1)% average fidelity in 450  μs, opening the door to the application of integrated state detection to quantum computing and sensing utilizing arrays of trapped ions.

Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620  μm. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Spatial Correlation between Fluctuating and Static Fields over Metal and Dielectric Substrates

We report spatially resolved measurements of static and fluctuating electric fields over conductive (Au) and nonconductive (SiO_{2}) surfaces. Using an ultrasensitive "nanoladder" cantilever probe to scan over these surfaces at distances of a few tens of nanometers, we record changes in the probe resonance frequency and damping that we associate with static and fluctuating fields, respectively. We find static and fluctuating fields to be spatially correlated. Furthermore, the fields are of similar magnitude for the two materials. We quantitatively describe the observed effects on the basis of trapped surface charges and dielectric fluctuations in an adsorbate layer. Our results are consistent with organic adsorbates significantly contributing to surface dissipation that affects nanomechanical sensors, trapped ions, superconducting resonators, and color centers in diamond.

Measurement of electric-field noise from interchangeable samples with a trapped-ion sensor

We demonstrate the use of a single trapped ion as a sensor to probe electric-field noise from interchangeable test surfaces. As proof of principle, we measure the magnitude and distance dependence of electric-field noise from two ion-trap-like samples with patterned Au electrodes. This trapped-ion sensor could be combined with other surface characterization tools to help elucidate the mechanisms that give rise to electric-field noise from ion-trap surfaces. Such noise presents a significant hurdle for performing large-scale trapped-ion quantum computations.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Surface science motivated by heating of trapped ions from the quantum ground state

For the past two and a half decades, anomalous heating of trapped ions from nearby electrode surfaces has continued to demonstrate unexpected results. Caused by electric-field noise, this heating of the ions' motional modes remains an obstacle for scalable quantum computation with trapped ions. One of the anomalous features of this electric-field noise is the reported nonmonotonic behavior in the heating rate when a trap is incrementally cleaned by ion bombardment. Motivated by this result, the present work reports on a surface analysis of a sample ion-trap electrode treated similarly with incremental doses of Ar+ ion bombardment. Kelvin probe force microscopy and x-ray photoelectron spectroscopy were used to investigate how the work functions on the electrode surface vary depending on the residual contaminant coverage between each treatment. It is shown that the as-fabricated Au electrode is covered with a hydrocarbon film that is modified after the first treatment, resulting in work functions and core-level binding energies that resemble that of atomic-like carbon on Au. Changes in the spatial distribution of work functions with each treatment, combined with a suggested phenomenological coverage and surface-potential roughness dependence to the heating, appear to be related to the nonmonotonic behavior previously reported.

High-Fidelity Two-Qubit Gates Using a Microelectromechanical-System-Based Beam Steering System for Individual Qubit Addressing

In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to four ions using radial modes. The ions are individually addressed by two tightly focused beams steered using microelectromechanical system mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors and discuss methods to further improve the gate fidelity towards values that are compatible with fault-tolerant quantum computation.

Convenient Real-Time Monitoring of the Contamination of Surface Ion Trap

Recent studies indicated that contamination by adatoms on the surface ion trap can generate contact potential, leading to fluctuations in patch potential. By investigating contamination induced by surface adatoms during a loading process, a direct physical image of the contamination process and the relationship between the capacitance change and the contamination from surface adatoms is examined theoretically and experimentally. From the relationship, the contamination by surface adatoms and the effect of in situ treatment process can be monitored by the capacitance between electrodes in real time. This study is foundational to further research on anomalous heating with practical applications in quantum information processing from surface ion traps.

Floquet-Engineered Vibrational Dynamics in a Two-Dimensional Array of Trapped Ions

We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range interion couplings and the related Peierls phase of the motional state. In our proof of principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions, and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical gauge fields.

Extending the Quantum Coherence of a Near-Surface Qubit by Coherently Driving the Paramagnetic Surface Environment

Surfaces enable useful functionalities for quantum systems, e.g., as interfaces to sensing targets, but often result in surface-induced decoherence where unpaired electron spins are common culprits. Here we show that the coherence time of a near-surface qubit is increased by coherent radio-frequency driving of surface electron spins, where we use a diamond nitrogen-vacancy (NV) center as a model qubit. This technique is complementary to other methods of suppressing decoherence and, importantly, requires no additional materials processing or control of the qubit. Further, by combining driving with the increased magnetic susceptibility of the double-quantum basis, we realize an overall fivefold sensitivity enhancement in NV magnetometry. Informed by our results, we discuss a path toward relaxation-limited coherence times for near-surface NV centers. The surface-spin driving technique presented here is broadly applicable to a wide variety of qubit platforms afflicted by surface-induced decoherence.

Interference in a Prototype of a Two-Dimensional Ion Trap Array Quantum Simulator

Trapped ions are a promising platform for envisioned quantum simulators, with outstanding results in one-dimensional ion crystals. However, theory requires not only interactions at long range, but also higher dimensionality. We operate a basic triangular array of three individually trapped ions based on scalable microfabrication technology. We demonstrate coherent coupling, tunable in real time and enabling interference in 2D, an essential building block for a reconfigurable quantum simulator. Mitigating motional heating will permit accessing the quantum regime and 2D experimental quantum simulations.

Crystallographic orientation dependence of work function: carbon adsorption on Au surfaces

We investigate the work function (WF) variation of different Au crystallographic surface orientations with carbon atom adsorption. Ab initio calculations within density-functional theory are performed on carbon deposited (100), (110), and (111) gold surfaces. The WF behaviour with carbon coverage for the different surface orientations is explained by the resultant electron charge density distributions. The dynamics of carbon adsorption at sub-to-one- monolayer (ML) coverage depends on the landscape of the potential energy surfaces. At higher ML coverage, because of adsorption saturation, the WF will have weak surface orientation dependence. This systematic study has consequential bearing on studies of electric-field noise emanating from polycrystalline gold ion-trap electrodes that have been largely employed in microfabricated electrodes.

Measuring Anomalous Heating in a Planar Ion Trap with Variable Ion-Surface Separation

Cold ions trapped in the vicinity of conductive surfaces experience heating of their oscillatory motion. Typically, the rate of this heating is orders of magnitude larger than expected from electric field fluctuations due to thermal motion of electrons in the conductors. This effect, known as anomalous heating, is not fully understood. One of the open questions is the heating rate's dependence on the ion-electrode separation. We present a direct measurement of this dependence in an ion trap of simple planar geometry. The heating rates are determined by taking images of a single ^{172}Yb^{+} ion's resonance fluorescence after a variable heating time and deducing the trapped ion's temperature from measuring its average oscillation amplitude. Assuming a power law for the heating rate versus ion-surface separation dependence, an exponent of -3.79±0.12 is measured.

Double-Quantum Spin-Relaxation Limits to Coherence of Near-Surface Nitrogen-Vacancy Centers

We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.

Fifteen years of cold matter on the atom chip: promise, realizations, and prospects

Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.

High-Fidelity Trapped-Ion Quantum Logic Using Near-Field Microwaves

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ^{43}Ca^{+} hyperfine "atomic clock" qubits (coherence time T_{2}^{*}≈50  s) using the oscillating magnetic field gradient produced by an integrated microwave electrode.

High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits

We demonstrate laser-driven two-qubit and single-qubit logic gates with respective fidelities 99.9(1)% and 99.9934(3)%, significantly above the ≈99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed-fidelity trade-off for the two-qubit gate, for gate times between 3.8  μs and 520  μs, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.

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.

Phonon arithmetic in a trapped ion system

Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.

Electric Field Cancellation on Quartz by Rb Adsorbate-Induced Negative Electron Affinity

We investigate the (0001) surface of single crystal quartz with a submonolayer of Rb adsorbates. Using Rydberg atom electromagnetically induced transparency, we investigate the electric fields resulting from Rb adsorbed on the quartz surface, and measure the activation energy of the Rb adsorbates. We show that the adsorbed Rb induces negative electron affinity (NEA) on the quartz surface. The NEA surface allows low energy electrons to bind to the surface and cancel the electric field from the Rb adsorbates. Our results will be important for integrating Rydberg atoms into hybrid quantum systems, as fundamental probes of atom-surface interactions, and for studies of 2D electron gases bound to surfaces.

Ground-State Cooling of a Trapped Ion Using Long-Wavelength Radiation

We demonstrate ground-state cooling of a trapped ion using radio-frequency (rf) radiation. This is a powerful tool for the implementation of quantum operations, where rf or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of n[over ¯]=0.13(4) after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the |n=0⟩ and |n=1⟩ Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost 2 orders of magnitude compared with our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.

Motional heating in a graphene-coated ion trap

Electric field noise originating from metal surfaces is a hindrance for a variety of microengineered systems, including for ions in microtraps, but is not well understood at the microscopic level. For trapped ions, it is manifested as motional-state decoherence inexplicable by thermal noise of electrodes alone, but likely surface-dependent. Here, we investigate the role of surface properties in motional heating by creating an ion trap with a unique exterior. Using single trapped-ion probes, we characterize copper electrodes covered in monolayer graphene, a material free of surface charge and dangling bonds. Surprisingly, we measure an average heating rate of 1020 ± 30 quanta/s, which is ∼100 times higher than typical for an uncoated trap operated under similar conditions. This may be related to hydrocarbon deposits on the surface, which could be monitored on graphene to potentially elucidate the mechanisms of motional heating on the atomic scale.

Tunable spin-spin interactions and entanglement of ions in separate potential wells

Quantum simulation--the use of one quantum system to simulate a less controllable one--may provide an understanding of the many quantum systems which cannot be modelled using classical computers. Considerable progress in control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our set-up we select one that entangles the internal states of the two ions with a fidelity of 0.82(1) (the digit in parentheses shows the standard error of the mean). Extension of this building block to a two-dimensional network, which is possible using ion-trap microfabrication processes, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient.

Control of the conformations of ion Coulomb crystals in a Penning trap

Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.

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.

Dissipation-assisted quantum information processing with trapped ions

We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating by showing that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for coherent or dissipative many-body quantum simulations.

Space-time crystals of trapped ions

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.