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Cryogenic environments benefit ion trapping experiments by offering lower motional heating rates, collision energies, and an ultrahigh vacuum (UHV) environment for maintaining long ion chains for extended periods of time. Mechanical vibrations caused by compressors in closed-cycle cryostats can introduce relative motion between the ion and the wavefronts of lasers used to manipulate the ions. Here, we present a novel ion trapping system where a commercial low-vibration closed-cycle cryostat is used in a custom monolithic enclosure. We measure mechanical vibrations of the sample stage using an optical interferometer, and observe a root-mean-square relative displacement of 2.4 nm and a peak-to-peak displacement of 17 nm between free-space beams and the trapping location. We packaged a surface ion trap in a cryopackage assembly that enables easy handling while creating a UHV environment for the ions. The trap cryopackage contains activated carbon getter material for enhanced sorption pumping near the trapping location, and source material for ablation loading. Using $^{171}$Yb$^{+}$ as our ion, we estimate the operating pressure of the trap as a function of package temperature using phase transitions of zig-zag ion chains as a probe. We measured the radial mode heating rate of a single ion to be 13 quanta/s on average. The Ramsey coherence measurements yield 330-ms coherence time for counter-propagating Raman carrier transitions using a 355-nm mode-locked pulse laser, demonstrating the high optical stability.

Objectives: The aim of this study was to examine the debate on the use of medical devices between Western Medicine and Korean Medicine, as this is one of the greatest conflicts in Korea's medical profession. Judicial precedents and interpretations of authority serve as regulations because medical affairs law states that Korean Medicine practices are ambiguous.Method: We conducted a search in the Korean RISS, OASIS, and DBPIA databases using several keywords associated with medical devices, Korean Medicine, and Korean Medicine Doctors. The search period was until November 5 2021. The retrieved papers were classified according to the selection and exclusion criteria by checking the title, abstract, and text. For precedents, searches were done regarding comprehensive legal information, etc., and in the case of non-disclosure precedents, we requested access to the precedents by web-court requests.Results: A total of 80 documents were found as a result of the search, and 13 publications were included in the study. The selected publications were classified and analyzed by this research team into Korean medicine, Western medicine, and legal or state agency research. In the existing literature and judgments, the arguments that played a major role changed depending on the time the judgment was made. “Social conventions”, “curriculum”, “academic principles”, and “health and hygiene dangers” were the key arguments.Conclusions: Further studies will be needed that can comprehensively arrange the existing literature and clinical results, and continuous study will be needed to verify that the use of medical devices by Korean medicine doctors is helpful for prognosis and accurate treatment of their patients.

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 modelled as residual $X\hat{\sigma}_{\phi}$ interaction and can be actively cancelled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk, yet only requires local control by driving rotations solely on the target 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 5-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians., Comment: 9 pages, 4 figures

Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum hardware. Here, we experimentally demonstrate an end-to-end pipeline that focuses on minimizing quantum resources while maintaining accuracy. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. The originally 20-qubit system is decomposed into 10 two-qubit problems, making it amenable to currently available hardware. Combining this decomposition with a qubit coupled cluster circuit ansatz, circuit optimization, and density matrix purification, we accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Our experimental results are an early demonstration of the potential for problem decomposition to accurately simulate large molecules on quantum hardware. Problem decomposition methods may help to overcome the size limitations of quantum hardware and allow largescale electronic structure simulations. Here, a method to simulate a ten-atom Hydrogen ring by decomposing it into smaller fragments that are amenable to a currently available trapped ion quantum computer is demonstrated experimentally.

High-fidelity two-qubit gates in quantum computers are often hampered by fluctuating experimental parameters. The effects of time-varying parameter fluctuations lead to coherent noise on the qubits, which can be suppressed by designing control signals with appropriate filter functions. Here, we develop filter functions for M{\o}lmer-S{\o}rensen gates of trapped-ion quantum computers that accurately predict the change in gate error due to small parameter fluctuations at any frequency. We then design the filter functions of frequency-modulated laser pulses, and compare this method with pulses that are robust to static offsets of the motional-mode frequencies. Experimentally, we measure the noise spectrum of the motional modes and use it for designing the filter functions, which improves the gate fidelity from 99.23(7)% to 99.55(7)% in a five-ion chain., Comment: 17 pages, 10 figures

In trapped-ion quantum computers, two-qubit entangling gates are generated by applying spin-dependent force which uses phonons to mediate interaction between the internal states of the ions. To maintain high-fidelity two-qubit gates under fluctuating experimental parameters, robust pulse-design methods are applied to remove the residual spin-motion entanglement in the presence of motional mode frequency drifts. Here we propose an improved pulse-design method that also guarantees the robustness of the two-qubit rotation angle against uniform mode frequency drifts by combining pulses with opposite sensitivity of the angle to mode frequency drifts. We experimentally measure the performance of the designed gates and see an improvement on both gate fidelity and gate performance under uniform mode frequency offsets., Comment: 10 pages, 11 figures

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 multi-mode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a 5-ion chain. This method can be extended to any system with Jaynes-Cummings type interactions., Comment: 11 pages, 8 figures

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this work, we design quantum machine learning algorithms to model copulas. We show that any copula can be naturally mapped to a multipartite maximally entangled state. A variational ansatz we christen as a `qopula' creates arbitrary correlations between variables while maintaining the copula structure starting from a set of Bell pairs for two variables, or GHZ states for multiple variables. As an application, we train a Quantum Generative Adversarial Network (QGAN) and a Quantum Circuit Born Machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables for historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to 8 qubits and show that our results outperform those obtained through equivalent classical generative learning. Further, we present theoretical arguments for exponential advantage in our model's expressivity over classical models based on communication and computational complexity arguments., 19 pages, 11 figures. v2: published version

Quantum machine learning has seen considerable theoretical and practical developments in recent years and has become a promising area for finding real world applications of quantum computers. In pursuit of this goal, here we combine state-of-the-art algorithms and quantum hardware to provide an experimental demonstration of a quantum machine learning application with provable guarantees for its performance and efficiency. In particular, we design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations, and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data.

The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 171Yb+ ions. We demonstrate average single-qubit gate fidelities of 99.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}%, average two-qubit-gate fidelities of 97.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}%, and SPAM errors of 0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}%. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% and 35\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}%, respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware., The growing complexity of quantum computing devices makes presents challenges for benchmarking their performance as previous, exhaustive approaches become infeasible. Here the authors characterise the quality of their 11-qubit device by successfully computing two quantum algorithms.

We have ubiquitous presence of computers today, ranging from simple controllers in modern appliances to smartphones in our pockets that provide a wide range of everyday services, to powerful supercomputers and large data centers that carry out the most computationally intensive tasks. These computational machines have a few things in common: for example, the information they handle is stored in bits (0 or 1), and the procedure for processing the information is specified by a program. A great deal is known about the limits of what such computational machines can and cannot do efficiently. There are many important computational problems that are believed to be very difficult to solve using even the most powerful computers, where the resource requirement—whether it is the size of the machine or the time it takes to finish the task—increases exponentially as a function of the problem size.

Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations. Our proposed resource-efficient pipeline combines problem decomposition techniques for compact molecular representations, circuit optimization methods for compilation, solving the eigenvalue problem on advanced quantum hardware, and error-mitigation techniques in post-processing the results. Using the density matrix embedding theory for compact representation, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms taking into account all electrons equally and explicitly in the electronic structure calculation. In our experiment, we simulated the largest molecular system on a quantum computer within chemical accuracy with respect to total molecular energy calculated by the full CI method. Our methods reduce the number of qubits required for high-accuracy quantum simulations by an order of magnitude in the present work, enabling the simulation of larger, more industrially relevant molecules using NISQ devices. They are further systematically improvable as devices’ computational capacity continues to grow.

We report measurements of the flux-integrated ν̅μ and ν̅μ + νμ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\mu^\pm$ and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$ and $\theta_{\mu}200~{\rm MeV}/c$, $\theta_{\pi}600~{\rm MeV}/c$, $\theta_{\rm p}

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2--10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21--22, 2019 in Alexandria, VA.

Two-qubit gates in trapped-ion quantum computers are generated by applying spin-dependent forces that temporarily entangle the internal state of the ion with its motion. Laser pulses are carefully designed to generate a maximally entangling gate between the ions while minimizing any residual entanglement between the motion and the ion. The quality of the gates suffers when the actual experimental parameters differ from the ideal case. Here, we improve the robustness of frequency-modulated M{\o}lmer-S{\o}rensen gates to motional mode-frequency offsets by optimizing the average performance over a range of systematic errors using batch optimization. We then compare this method with frequency-modulated gates optimized for ideal parameters that include an analytic robustness condition. Numerical simulations show good performance up to 12 ions, and the method is experimentally demonstrated on a two-ion chain.

We achieve fast, nondestructive quantum-state readout via fluorescence detection of a single $^{87}\mathrm{Rb}$ atom in the $5{S}_{1/2}$ $(F=2)$ ground state held in an optical dipole trap. The atom is driven by linearly polarized readout laser beams, making the scheme insensitive to the distribution of atomic population in magnetic sublevels. We demonstrate a readout fidelity of $97.6\ifmmode\pm\else\textpm\fi{}0.2%$ in a readout time of $160\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ with the atom retained in $g97%$ of the trials, representing an advancement over other magnetic-state-insensitive techniques. We demonstrate that the $F=2$ state is partially protected from optical pumping by the distribution of the dipole matrix elements for the various transitions and the ac-Stark shifts from the optical trap. Our results are likely to find application in neutral-atom quantum computing and simulation.

We thank the J-PARC staff for superb accelerator performance. We thank the CERN NA61/SHINE Collaboration for providing valuable particle production data. We acknowledge the support of MEXT, Japan; NSERC (Grant No. SAPPJ-2014-00031), the NRC and CFI, Canada; the CEA and CNRS/IN2P3, France; the DFG, Germany; the INFN, Italy; the National Science Centre and Ministry of Science and Higher Education, Poland; the RSF (Grant No. 19-12-00325) and the Ministry of Science and Higher Education, Russia; MINECO and ERDF funds, Spain; the SNSF and SERI, Switzerland; the STFC, UK; and the DOE, USA. We also thank CERN for the UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the WestGrid and SciNet consortia in Compute Canada, and GridPP in the United Kingdom. In addition, participation of individual researchers and institutions has been further supported by funds from the ERC (FP7), “la Caixa” Foundation (ID 100010434, fellowship code LCF/BQ/IN17/11620050), the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska- Curie Grants Agreement No. 713673 and No. 754496, and H2020 Grant No. RISE-GA822070-JENNIFER2 2020 and No. RISE-GA872549-SK2HK; the JSPS, Japan; the Royal Society, UK; French ANR Grant No. ANR-19- CE31-0001; and the DOE Early Career programme, USA.

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.

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.

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 4 ions using radial modes. The ions are individually addressed by two tightly focused beams steered using micro-electromechanical system (MEMS) 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., 8 pages, 4 figures