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

Individually addressed entangling gates in a two-dimensional ion crystal

Two-dimensional (2D) ion crystals may represent a promising path to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal.

On-Surface Atomic Scale Qubit Platform

Recent advances in scanning probe microscopy combined with electron spin resonance have revealed that localized electron spins on or near surfaces can be utilized as building blocks for the bottom-up assembly of functional quantum-coherent nanostructures. In this perspective, we review the recent advances, lay out advantages of this platform and outline the challenges that lie ahead on the way to the application of on-surface atomic spins to quantum information science and quantum computing.

Spectral Hole-Burning Studies of a Mononuclear Eu(III) Complex Reveal Narrow Optical Linewidths of the 5D0→7F0 Transition and Seconds Long Nuclear Spin Lifetimes

Coordination complexes of rare-earth ions (REI) show optical transitions with narrow linewidths enabling the creation of coherent light-matter interfaces for quantum information processing (QIP) applications. Among the REI-based complexes, Eu(III) complexes showing the 5D0→7F0 transition are of interest for QIP applications due to the narrow linewidths associated with the transition. Herein, we report on the synthesis, structure, and optical properties of a novel Eu(III) complex and its Gd(III) analogue composed of 2,9-bis(pyrazol-1-yl)-1,10-phenanthroline (dpphen) and three nitrate (NO3) ligands. The Eu(III) complex-[Eu(dpphen)(NO3)3]-showed sensitized metal-centred emission (5D0→7FJ; J=0,1,2,3, 4, 5, or 6) in the visible region, upon irradiation of the ligand-centred band at 369 nm, with the 5D0→7F0 transition centred at 580.9 nm. Spectral hole-burning (SHB) studies of the complex with stoichiometric Eu(III) concentration revealed a narrow homogeneous linewidth (Γh) of 1.55 MHz corresponding to a 0.205 μs long optical coherence lifetime (T2opt). Remarkably, long nuclear spin lifetimes (T1spin) of up to 41 s have been observed for the complex. The narrow optical linewidths and long T1spin lifetimes obtained for the Eu(III) complex showcase the utility of Eu(III) complexes as tuneable, following molecular engineering principles, coherent light-matter interfaces for QIP applications.

Electromagnetically Induced Transparency Cooling of High-Nuclear-Spin Ions

We report the electromagnetically induced transparency (EIT) cooling of ^{137}Ba^{+} ions with a nuclear spin of I=3/2, which are a good candidate of qubits for future large-scale trapped-ion quantum computing. EIT cooling of atoms or ions with a complex ground-state level structure is challenging due to the lack of an isolated Λ system, as the population can escape from the Λ system to reduce the cooling efficiency. We overcome this issue by leveraging an EIT pumping laser to repopulate the cooling subspace, ensuring continuous and effective EIT cooling. We cool the two radial modes of a single ^{137}Ba^{+} ion to average motional occupations of 0.08(5) and 0.15(7), respectively. Using the same laser parameters, we also cool all the ten radial modes of a five-ion chain to near their ground states. Our approach can be adapted to atomic species possessing similar level structures. It allows engineering of the EIT Fano-like spectrum, which can be useful for simultaneous cooling of modes across a wide frequency range, aiding in large-scale trapped-ion quantum information processing.

Future Potential of Quantum Computing and Simulations in Biological Science

The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.

Fast Photon-Mediated Entanglement of Continuously Cooled Trapped Ions for Quantum Networking

We entangle two cotrapped atomic barium ion qubits by collecting single visible photons from each ion through in vacuo 0.8 NA objectives, interfering them through an integrated fiber beam splitter and detecting them in coincidence. This projects the qubits into an entangled Bell state with an observed fidelity lower bound of F>94%. We also introduce an ytterbium ion for sympathetic cooling to remove the need for recooling interruptions and achieve a continuous entanglement rate of 250  s^{-1}.

Low cross-talk optical addressing of trapped-ion qubits using a novel integrated photonic chip

Individual optical addressing in chains of trapped atomic ions requires the generation of many small, closely spaced beams with low cross-talk. Furthermore, implementing parallel operations necessitates phase, frequency, and amplitude control of each individual beam. Here, we present a scalable method for achieving all of these capabilities using a high-performance integrated photonic chip coupled to a network of optical fibre components. The chip design results in very low cross-talk between neighbouring channels even at the micrometre-scale spacing by implementing a very high refractive index contrast between the channel core and cladding. Furthermore, the photonic chip manufacturing procedure is highly flexible, allowing for the creation of devices with an arbitrary number of channels as well as non-uniform channel spacing at the chip output. We present the system used to integrate the chip within our ion trap apparatus and characterise the performance of the full individual addressing setup using a single trapped ion as a light-field sensor. Our measurements showed intensity cross-talk below ~10-3 across the chip, with minimum observed cross-talk as low as ~10-5.

Preparing pure 43 Ca + samples in an ion trap with photoionization and parametric excitations

We present a practical scheme for the efficient preparation of laser-cooled43 Ca+ ions in an ion trap. Our approach integrates two well-established methods: isotope-selective photoionization and isotope-specific parametric excitation. Drawing inspiration from the individual merits of each method, we have successfully integrated these techniques to prepare extended chains of43 Ca+ ions, overcoming the challenge posed by their low natural abundance of 0.135% in a natural source. Furthermore, we explore the subtleties of our scheme, focusing on the influence of different factors on the purification process. Our investigation contributes to a broader understanding of the technique and highlights the adaptability of established methods in addressing specific isotopic challenges.

A Globally Accurate Neural Network Potential Energy Surface and Quantum Dynamics Studies on Be+(2S) + H2/D2 → BeH+/BeD+ + H/D Reactions

Chemical reactions between Be+ ions and H2 molecules have significance in the fields of ultracold chemistry and astrophysics, but the corresponding dynamics studies on the ground-state reaction have not been reported because of the lack of a global potential energy surface (PES). Herein, a globally accurate ground-state BeH2+ PES is constructed using the neural network model based on 18,657 ab initio points calculated by the multi-reference configuration interaction method with the aug-cc-PVQZ basis set. On the newly constructed PES, the state-to-state quantum dynamics calculations of the Be+(2S) + H2(v0 = 0; j0 = 0) and Be+(2S) + D2(v0 = 0; j0 = 0) reactions are performed using the time-dependent wave packet method. The calculated results suggest that the two reactions are dominated by the complex-forming mechanism and the direct abstraction process at relatively low and high collision energies, respectively, and the isotope substitution has little effect on the reaction dynamics characteristics. The new PES can be used to further study the reaction dynamics of the BeH2+ system, such as the effects of rovibrational excitations and alignment of reactant molecules, and the present dynamics data could provide an important reference for further experimental studies at a finer level.

Eliminating Qubit-Type Cross-Talk in the omg Protocol

The omg protocol is a promising paradigm that uses multiple, application-specific, qubit subspaces within the Hilbert space of each single atom during quantum information processing. A key assumption for omg operation is that a subspace can be accessed independently without deleterious effects on information stored in other subspaces. We find that intensity noise during laser-based quantum gates in one subspace can cause decoherence in other subspaces, potentially complicating omg operation. We show, however, that a magnetic-field-induced vector light shift can be used to eliminate this source of decoherence. As this technique simply requires choosing a specific, magnetic field-dependent polarization for the gate lasers, it is straightforward to implement and potentially helpful for omg-based quantum technology.

Low phase noise cavity transmission self-injection locked diode laser system for atomic physics experiments

Lasers with high spectral purity are indispensable for optical clocks and for the coherent manipulation of atomic and molecular qubits in applications such as quantum computing and quantum simulation. While the stabilization of such lasers to a reference can provide a narrow linewidth, the widely used diode lasers exhibit fast phase noise that prevents high-fidelity qubit manipulation. In this paper, we demonstrate a self-injection locked diode laser system that utilizes a high-finesse cavity. This cavity not only provides a stable resonance frequency, it also acts as a low-pass filter for phase noise beyond the cavity linewidth of around 100 kHz, resulting in low phase noise from dc to the injection lock limit. We model the expected laser performance and benchmark it using a single trapped 40Ca+-ion as a spectrum analyzer. We show that the fast phase noise of the laser at relevant Fourier frequencies of 100 kHz to >2 MHz is suppressed to a noise floor of between -110 dBc/Hz and -120 dBc/Hz, an improvement of 20 to 30 dB over state-of-the-art Pound-Drever-Hall-stabilized extended-cavity diode lasers. This strong suppression avoids incoherent (spurious) spin flips during manipulation of optical qubits and improves laser-driven gates when using diode lasers in applications involving quantum logic spectroscopy, quantum simulation, and quantum computation.

Microgram BaCl2 ablation targets for trapped ion experiments

Trapped ions for quantum information processing have been an area of intense study due to the extraordinarily high fidelity operations that have been reported experimentally. Specifically, barium trapped ions have been shown to have exceptional state-preparation and measurement fidelities. The 133Ba+ (I = 1/2) isotope in particular is a promising candidate for large-scale quantum computing experiments. However, a major pitfall with this isotope is that it is radioactive and is thus generally used in microgram quantities to satisfy safety regulations. We describe a new method for creating microgram barium chloride (BaCl2) ablation targets for use in trapped ion experiments and compare our procedure to previous methods. We outline two recipes for the fabrication of ablation targets that increase the production of neutral atoms for isotope-selective loading of barium ions. We show that heat-treatment of the ablation targets greatly increases the consistency at which neutral atoms can be produced, and we characterize the uniformity of these targets using trap-independent techniques such as energy dispersive x-ray spectroscopy and neutral fluorescence collection. Our comparison between fabrication techniques and the demonstration of consistent neutral fluorescence paves a path toward reliable loading of 133Ba+ in surface traps and opens opportunities for scalable quantum computing with this isotope.

Penning micro-trap for quantum computing

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, because of high-fidelity quantum gates and long coherence times1-3. However, the use of radio-frequencies presents several challenges to scaling, including requiring compatibility of chips with high voltages4, managing power dissipation5 and restricting transport and placement of ions6. Here we realize a micro-fabricated Penning ion trap that removes these restrictions by replacing the radio-frequency field with a 3 T magnetic field. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the quantum charge-coupled device architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

Ion trap with in-vacuum high numerical aperture imaging for a dual-species modular quantum computer

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10(1)% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics

Modern biological science is trying to solve the fundamental complex problems of molecular biology, which include protein folding, drug discovery, simulation of macromolecular structure, genome assembly, and many more. Currently, quantum computing (QC), a rapidly emerging technology exploiting quantum mechanical phenomena, has developed to address current significant physical, chemical, biological issues, and complex questions. The present review discusses quantum computing technology and its status in solving molecular biology problems, especially in the next-generation computational biology scenario. First, the article explained the basic concept of quantum computing, the functioning of quantum systems where information is stored as qubits, and data storage capacity using quantum gates. Second, the review discussed quantum computing components, such as quantum hardware, quantum processors, and quantum annealing. At the same time, article also discussed quantum algorithms, such as the grover search algorithm and discrete and factorization algorithms. Furthermore, the article discussed the different applications of quantum computing to understand the next-generation biological problems, such as simulation and modeling of biological macromolecules, computational biology problems, data analysis in bioinformatics, protein folding, molecular biology problems, modeling of gene regulatory networks, drug discovery and development, mechano-biology, and RNA folding. Finally, the article represented different probable prospects of quantum computing in molecular biology.

Ultrahigh-fidelity spatial mode quantum gates in high-dimensional space by diffractive deep neural networks

While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate's performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.

Sideband cooling of a trapped ion in strong sideband coupling regime

Conventional theoretical studies on the ground-state laser cooling of a trapped ion have mostly focused on the weak sideband coupling (WSC) regime, where the cooling rate is inverse proportional to the linewidth of the excited state. In a recent work [New J. Phys.23, 023018 (2021)10.1088/1367-2630/abe273], we proposed a theoretical framework to study the ground state cooling of a trapped ion in the strong sideband coupling (SSC) regime, under the assumption of a vanishing carrier transition. Here we extend this analysis to more general situations with nonvanishing carrier transitions, where we show that by properly tuning the coupling lasers a cooling rate proportional to the linewidth can be achieved. Our theoretical predictions closely agree with the corresponding exact solutions in the SSC regime, which provide an important theoretical guidance for sideband cooling experiments.

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

High performance on-chip polarization beam splitter at visible wavelengths based on a silicon nitride small-sized ridge waveguide

Due to sensitive scaling of the wavelength and the visible-light absorption properties with the device dimension, traditional passive silicon photonic devices with asymmetric waveguide structures cannot achieve polarization control at the visible wavelengths. In this work, a simple and small polarization beam splitter (PBS) for a broad visible-light band, using a tailored silicon nitride (Si3N4) ridge waveguide, is presented, which is based on the distinct optical distribution of two fundamental orthogonal polarized modes in the ridge waveguide. The bending loss for different bending radii and the optical coupling properties of the fundamental modes for different Si3N4 ridge waveguide configurations are analyzed. A PBS composed of a bending ridge waveguide structure and a triple-waveguide directional coupler was fabricated on the Si3N4 thin film. The TM excitation of the device based on a bending ridge waveguide structure shows a polarization extinction ratio (PER) of ≥ 20 dB with 33 nm bandwidth (624-657 nm) and insertion loss (IL) ≤ 1 dB at the through port. The TE excitation of the device, based on a triple-waveguide directional coupler with coupling efficiency distinction between the TE0 and TM0 modes, shows a PER of ≥ 18 dB with 50 nm bandwidth (580-630 nm) and insertion loss (IL) ≤ 1 dB at the cross port. The on-chip Si3N4 PBS device is found to possess the highest known PER at a visible broadband range and small (43 µm) footprint. It should be useful for novel photonic circuit designs and further exploration of Si3N4 PBSs.

Impact of Imperfect Timekeeping on Quantum Control

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter that no physical clock can ever perfectly characterize. In this Letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the circuit complexity they are able to achieve within circuit-based quantum computation. We do this by deriving an upper bound on the average gate fidelity achievable under imperfect timekeeping for a general class of random circuits. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.

Fast, High-Fidelity Addressed Single-Qubit Gates Using Efficient Composite Pulse Sequences

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for ^{43}Ca^{+} hyperfine "atomic clock" qubits in a cryogenic (100 K) surface trap. For a single qubit, we benchmark an error of 1.5×10^{-6} per Clifford gate (implemented using 600 ns π/2 pulses). For 2 qubits in the same trap zone (ion separation 5  μm), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error 3.4×10^{-5} per addressed π/2 gate. The scheme scales theoretically to larger numbers of qubits in a single register.

Raman Scattering Errors in Stimulated-Raman-Induced Logic Gates in ^{133}Ba^{+}

^{133}Ba^{+} is illuminated by a laser that is far detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental atomic physics limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering.

Coherent Control of Trapped-Ion Qubits with Localized Electric Fields

We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multizone trap by simultaneously applying an electric field and a spin-dependent gradient. Both the phase and amplitude of the effective single-qubit rotation depend on the electric field, which can be localized to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic-field gradients in a surface-electrode ion trap, and measure the localization of the electric field.

Dielectrics for Two-Dimensional Transition-Metal Dichalcogenide Applications

Despite over a decade of intense research efforts, the full potential of two-dimensional transition-metal dichalcogenides continues to be limited by major challenges. The lack of compatible and scalable dielectric materials and integration techniques restrict device performances and their commercial applications. Conventional dielectric integration techniques for bulk semiconductors are difficult to adapt for atomically thin two-dimensional materials. This review provides a brief introduction into various common and emerging dielectric synthesis and integration techniques and discusses their applicability for 2D transition metal dichalcogenides. Dielectric integration for various applications is reviewed in subsequent sections including nanoelectronics, optoelectronics, flexible electronics, valleytronics, biosensing, quantum information processing, and quantum sensing. For each application, we introduce basic device working principles, discuss the specific dielectric requirements, review current progress, present key challenges, and offer insights into future prospects and opportunities.

Native qudit entanglement in a trapped ion quantum processor

Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.

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.

Robust Quantum Memory in a Trapped-Ion Quantum Network Node

We integrate a long-lived memory qubit into a mixed-species trapped-ion quantum network node. Ion-photon entanglement first generated with a network qubit in ^{88}Sr^{+} is transferred to ^{43}Ca^{+} with 0.977(7) fidelity, and mapped to a robust memory qubit. We then entangle the network qubit with a second photon, without affecting the memory qubit. We perform quantum state tomography to show that the fidelity of ion-photon entanglement decays ∼70 times slower on the memory qubit. Dynamical decoupling further extends the storage duration; we measure an ion-photon entanglement fidelity of 0.81(4) after 10 s.

Efficient numerical approach to high-fidelity phase-modulated gates in long chains of trapped ions

Almost every quantum circuit is built with two-qubit gates in the current stage, which are crucial to the quantum computing in any platform. The entangling gates based on Mølmer-Sørensen schemes are widely exploited in the trapped-ion system, with the utilization of the collective motional modes of ions and two laser-controlled internal states, which are served as qubits. The key to realize high-fidelity and robust gates is the minimization of the entanglement between the qubits and the motional modes under various sources of errors after the gate operation. In this work, we propose an efficient numerical method to search high-quality solutions for phase-modulated pulses. Instead of directly optimizing a cost function, which contains the fidelity and the robustness of the gates, we convert the problem to the combination of linear algebra and the solution to quadratic equations. Once a solution with the gate fidelity of 1 is found, the laser power can be further reduced while searching on the manifold where the fidelity remains 1. Our method largely overcomes the problem of the convergence and is shown to be effective up to 60 ions, which suffices the need of the gate design in current trapped-ion experiments.

Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10-6 logical error per cycle floor set by a single high-energy event (1.6 × 10-7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

Robust Two-Qubit Gates for Trapped Ions Using Spin-Dependent Squeezing

Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.

99.92%-Fidelity cnot Gates in Solids by Noise Filtering

Inevitable interactions with the reservoir largely degrade the performance of entangling gates, which hinders practical quantum computation from coming into existence. Here, we experimentally demonstrate a 99.920(7)%-fidelity controlled-not gate by suppressing the complicated noise in a solid-state spin system at room temperature. We found that the fidelity limited at 99% in previous works results from considering only static classical noise, and, thus, in this work, a complete noise model is constructed by also considering the time dependence and the quantum nature of the spin bath. All noises in the model are dynamically corrected by an exquisitely designed shaped pulse, giving the resulting error below 10^{-4}. The residual gate error is mainly originated from the longitudinal relaxation and the waveform distortion that can both be further reduced technically. Our noise-resistant method is universal and will benefit other solid-state spin systems.

Crosstalk Suppression in Individually Addressed Two-Qubit Gates in a Trapped-Ion Quantum Computer

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual Xσ[over ^]_{ϕ} interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians.

High Fidelity State Preparation and Measurement of Ion Hyperfine Qubits with I>1/2

We present a method for achieving high fidelity state preparation and measurement (SPAM) using trapped ion hyperfine qubits with nuclear spins higher than I=1/2. The ground states of these higher nuclear spin isotopes do not afford a simple frequency-selective state preparation scheme. We circumvent this limitation by stroboscopically driving strong and weak transitions, blending fast optical pumping using dipole transitions, and narrow microwave or optical quadrupole transitions. We demonstrate this method with the I=3/2 isotope ^{137}Ba^{+} to achieve a SPAM infidelity of (9.0±1.3)×10^{-5} (-40.5±0.6  dB), facilitating the use of a wider range of ion isotopes with favorable wavelengths and masses for quantum computation.

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

Interplay of magnetic states and hyperfine fields of iron dimers on MgO(001)

Individual nuclear spin states can have very long lifetimes and could be useful as qubits. Progress in this direction was achieved on MgO/Ag(001) via detection of the hyperfine interaction (HFI) of Fe, Ti and Cu adatoms using scanning tunneling microscopy. Previously, we systematically quantified from first-principles the HFI for the whole series of 3d transition adatoms (Sc-Cu) deposited on various ultra-thin insulators, establishing the trends of the computed HFI with respect to the filling of the magnetic s- and d-orbitals of the adatoms and on the bonding with the substrate. Here we explore the case of dimers by investigating the correlation between the HFI and the magnetic state of free standing Fe dimers, single Fe adatoms and dimers deposited on a bilayer of MgO(001). We find that the magnitude of the HFI can be controlled by switching the magnetic state of the dimers. For short Fe-Fe distances, the antiferromagnetic state enhances the HFI with respect to that of the ferromagnetic state. By increasing the distance between the magnetic atoms, a transition toward the opposite behavior is observed. Furthermore, we demonstrate the ability to substantially modify the HFI by atomic control of the location of the adatoms on the substrate. Our results establish the limits of applicability of the usual hyperfine hamiltonian and we propose an extension based on multiple scattering processes.

Observation of supersymmetry and its spontaneous breaking in a trapped ion quantum simulator

Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.

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.

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.

Transport-Enabled Entangling Gate for Trapped Ions

We implement a 2-qubit entangling Mølmer-Sørensen interaction by transporting two cotrapped ^{40}Ca^{+} ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a constant Doppler shift during the transport, which uses fine temporal adjustment of the moving confinement potential. The fixed interaction duration of the ions transported through the laser beam as well as the dynamically changing ac Stark shift require alterations to the calibration procedures used for a stationary gate. We use the interaction to produce Bell states with fidelities commensurate to those of stationary gates performed in the same system. This result establishes the feasibility of actively incorporating ion transport into quantum information entangling operations.

Fast universal quantum gate above the fault-tolerance threshold in silicon

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction¹. One of the most promising error correction codes is the surface code², which requires universal gate fidelities exceeding an error correction threshold of 99 per cent³. Among the many qubit platforms, only superconducting circuits⁴, trapped ions⁵ and nitrogen-vacancy centres in diamond⁶ have delivered this requirement. Electron spin qubits in silicon^7-15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation¹⁶. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers.

Neural network potential energy surface and quantum dynamics studies for the Ca+(2S) + H2 → CaH+ + H reaction

Reactive collisions of Ca+ ion with H2 molecule play a crucial role in ultracold chemistry, quantum information and other cutting-edge fields, and have been widely concerned experimentally, but the corresponding...

Trapped Ion Quantum Computing Using Optical Tweezers and Electric Fields

We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground-state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.

Experimental Realization of Multi-ion Sympathetic Cooling on a Trapped Ion Crystal

Trapped ions are one of the leading platforms in quantum information science. For quantum computing with large circuit depth and quantum simulation with long evolution time, it is of crucial importance to cool large ion crystals at runtime without affecting the internal states of the computational qubits, thus the necessity of sympathetic cooling. Here, we report multi-ion sympathetic cooling on a long ion chain using a narrow cooling beam focused on two adjacent ions, and optimize the choice of the cooling ions according to the collective oscillation modes of the chain. We show that, by cooling a small fraction of ions, cooling effects close to the global Doppler cooling limit can be achieved. This experiment therefore demonstrates an important enabling step for quantum information processing with large ion crystals.

High-Fidelity Bell-State Preparation with ^{40}Ca^{+} Optical Qubits

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35  μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.

Exploiting Dynamic Quantum Circuits in a Quantum Algorithm with Superconducting Qubits

To date, quantum computation on real, physical devices has largely been limited to simple, time-ordered sequences of unitary operations followed by a final projective measurement. As hardware platforms for quantum computing continue to mature in size and capability, it is imperative to enable quantum circuits beyond their conventional construction. Here we break into the realm of dynamic quantum circuits on a superconducting-based quantum system. Dynamic quantum circuits not only involve the evolution of the quantum state throughout the computation but also periodic measurements of qubits midcircuit and concurrent processing of the resulting classical information on timescales shorter than the execution times of the circuits. Using noisy quantum hardware, we explore one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version, which exploits dynamic circuits, and compare the results to a nonadaptive implementation of the same algorithm. We demonstrate that the version of real-time quantum computing with dynamic circuits can yield results comparable to an approach involving classical asynchronous postprocessing, thus opening the door to a new realm of available algorithms on real quantum systems.

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 operations5-7 and single-qubit rotations8 so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams9-12 or by moving ions with respect to laser beams13-15, but at lower fidelities. Laser-free entangling methods16-20 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 photonics21,22 and trap-integrated photon detectors for qubit readout23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.