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arXiv 2023年

作者： Shammah, Nathan Roy, Anurag Saha Almudever, Carmen G. Bourdeauducq, Sébastien Butko, Anastasiia Cancelo, Gustavo Clark, Susan M. Heinsoo, Johannes Henriet, Loïc Huang, Gang Jurczak, Christophe Kotilahti, Janne Landra, Alessandro LaRose, Ryan Mari, Andrea Nowrouzi, Kasra Ockeloen-Korppi, Caspar Prawiroatmodjo, Guen Siddiqi, Irfan Zeng, William J. Unitary Fund San FranciscoCA94104 United States Qruise GmbH Saarbruecken66113 Germany Technical University of Valencia Spain M-Labs Limited North Point Hong Kong Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Fermi National Accelerator Laboratory BataviaIL60510 United States Sandia National Laboratories AlbuquerqueNM87123 United States IQM Quantum Computers Espoo02150 Finland PASQAL 7 rue Leonard de Vinci Massy91300 France Accelerator Technology and Applied Physics Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Quantonation Paris75010 France Center for Quantum Computing Science and Engineering Michigan State University East LansingMI48824 United States School of Science and Technology Università di Camerino Camerino62032 Italy Microsoft Quantum RedmondWA98052 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States

Quantum technologies such as communications, computing, and sensing offer vast opportunities for advanced research and development. While an open-source ethos currently exists within some quantum technologies, especially in quantum computer programming, we argue that there are additional advantages in developing open quantum hardware (OQH). Open quantum hardware encompasses open-source software for the control of quantum devices in labs, blueprints and open-source toolkits for chip design and other hardware components, as well as openly-accessible testbeds and facilities that allow cloud-access to a wider scientific community. We provide an overview of current projects in the OQH ecosystem, identify gaps, and make recommendations on how to close them today. More open quantum hardware would accelerate technology transfer to and growth of the quantum industry and increase accessibility in science. © 2023, CC BY.

关键词： technology transfer

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An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

arXiv

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arXiv 2021年

作者： Lee, Chak Shing Hamon, François P. Castelletto, Nicola Vassilevski, Panayot S. White, Joshua A. Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States TotalEnergies E&P Research and Technology HoustonTX77002 United States Atmospheric Earth and Energy Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR97201 United States

MSC Codes 65M55, 65M08A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a natural generalization of the upwind flux can be evaluated directly on coarse levels using the precomputed coarse flux basis vectors. The resulting solver is applicable to problems discretized on general unstructured grids. The performance of the proposed nonlinear multigrid solver in comparison with the standard single level Newton's method is demonstrated through challenging numerical examples. It is observed that the proposed solver is robust for highly nonlinear problems and clearly outperforms Newton's method in the case of high Courant-Friedrichs-Lewy (CFL) numbers. Copyright © 2021, The Authors. All rights reserved.

关键词： Two phase flow

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Two-loop non-planar hexa-box integrals with one massive leg

arXiv

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arXiv 2022年

作者： Kardos, Adam Papadopoulos, Costas G. Smirnov, Alexander V. Syrrakos, Nikolaos Wever, Christopher University of Debrecen Faculty of Science and Technology Department of Experimental Physics PO Box 105 Debrecen4010 Hungary Institute of Nuclear and Particle Physics NCSR Demokritos Patr. Grigoriou E’ & 27 Neapoleos Str Agia Paraskevi15341 Greece Research Computing Center Moscow State University Moscow119991 Russia Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia Physik-Department Technische Universität München James-Franck-Str. 1 Garching85748 Germany Physics Division National Technical University of Athens Zografou Campus Athens15780 Greece

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots. The results are relevant to the study of NNLO QCD corrections for W, Z and Higgs-boson production in association with two hadronic jets. Copyright © 2022, The Authors. All rights reserved.

关键词： Bosons

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Randomized Compiling for Scalable Quantum computing on a Noisy Superconducting Quantum Processor

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Physical Review X 2021年第4期11卷 041039-041039页

作者： Akel Hashim Ravi K. Naik Alexis Morvan Jean-Loup Ville Bradley Mitchell John Mark Kreikebaum Marc Davis Ethan Smith Costin Iancu Kevin P. O’Brien Ian Hincks Joel J. Wallman Joseph Emerson Irfan Siddiqi Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Graduate Group in Applied Science and Technology University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02142 USA Quantum Benchmark Inc. Kitchener Ontario N2H 5G5 Canada Keysight Technologies Canada Kanata Ontario K2K 2W5 Canada Institute for Quantum Computing and Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.

关键词： Quantum algorithms Quantum benchmarking Quantum control Quantum information with solid state qubits

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The white rat of numerical reproducibility

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AIP Conference Proceedings 2021年第1期2365卷

作者： Michael Mascagni Departments of Computer Science Mathematics and Scientific Computing Florida State University Tallahassee FL 32306-4530 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg MD 20899-8910 USA

We explore an application from the author’s work in neuroscience. A code used to investigate neural development modeled 100 neurons with all-to-all excitatory connectivity. We used a simple ordinary differential equation system to model each neuron, and this 100-neuron model was used to produce a paper published in the Journal of Neurophysiology. Later a colleague used our code to continue this work, and found he could not reproduce our results. This lead us to thoroughly investigate this code and we discovered that it offered many different ways to thwart reproducibility that could be explained by round-off error arising from floating-point *** reproducibility is considered a task that directly follows from the determinism in computations. However, reproducibility has become an intense concern and and issue for research. In fact, the author developed an series of international workshops on numerical reproducibility and computational reproducibility that is now a regular offering at the annual international supercomputing conferences. We will show how this particular code provides a lack of reproducibility from the following three mechanisms: (i) the introduction of floating-point errors in an inner product; (ii) introduction of floating-point errors at each an increasing number of time steps during temporal refinement (ii); and (iii) differences in the output of library mathematical functions at the level of round-off error. This code’s sensitivity makes it a very powerful tool to explore many different manifestations of numerical reproducibility. However, this code is by no means exceptional, as in neuroscience these types of models are used extensively to gain insights on the functioning of the nervous system. In addition, these types of models are widely used in many other fields of study as they just nonlinear evolution equations.

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Collective Neutrino Oscillations in Three Flavors on Qubit and Qutrit Processors

arXiv

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arXiv 2025年

作者： Spagnoli, Luca Goss, Noah Roggero, Alessandro Rrapaj, Ermal Cervia, Michael J. Patwardhan, Amol V. Naik, Ravi K. Balantekin, A. Baha Younis, Ed Santiago, David I. Siddiqi, Irfan Aldaihan, Sheakha Physics Department University of Trento Via Sommarive 14 TrentoI-38123 Italy INFN-TIFPA Trento Institute of Fundamental Physics and Applications Trento Italy Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Physics University of California BerkeleyCA94720 United States RIKEN iTHEMS Saitama Wako351-0198 Japan Department of Physics University of Washington SeattleWA98195 United States School of Physics and Astronomy University of Minnesota MinneapolisMN55455 United States Department of Physics New York Institute of Technology New YorkNY10023 United States Department of Physics University of Wisconsin MadisonWI53706 United States Department of Physics Gettysburg College GettysburgPA17325 United States

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup. Copyright © 2025, The Authors. All rights reserved.

关键词： Neutrons

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Risk-based decision making: estimands for sequential prediction under interventions

arXiv

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arXiv 2023年

作者： Luijken, Kim Morzywolek, Pawel van Amsterdam, Wouter Cinà, Giovanni Hoogland, Jeroen Keogh, Ruth Krijthe, Jesse Magliacane, Sara van Ommen, Thijs Peek, Niels Putter, Hein van Smeden, Maarten Sperrin, Matthew Wang, Junfeng Weir, Daniala Didelez, Vanessa van Geloven, Nan Department of Epidemiology Julius Center for Health Sciences and Primary Care University Medical Center Utrecht Utrecht Netherlands Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Department of Statistics University of Washington Seattle United States Department of Medical Informatics Amsterdam University Medical Centers Amsterdam Netherlands Institute for Logic Language and Computation University of Amsterdam Amsterdam Netherlands Pacmed Amsterdam Netherlands Department of Epidemiology and Data Science Amsterdam University Medical Centers Amsterdam Netherlands Department of Medical Statistics London School of Hygiene & Tropical Medicine Keppel Street London United Kingdom Pattern Recognition and Bio-Informatics Group EEMCS Delft University of Technology Delft Netherlands Amsterdam Machine Learning Lab University of Amsterdam Amsterdam Netherlands Department of Information and Computing Sciences Utrecht University Utrecht Netherlands Division of Informatics Imaging and Data Science Faculty of Biology Medicine and Health University of Manchester Manchester Academic Health Science Centre Manchester United Kingdom Department of Biomedical Data Sciences Leiden University Medical Center Leiden Netherlands Division of Pharmacoepidemiology and Clinical Pharmacology Department of Pharmaceutical Sciences Utrecht University Utrecht Netherlands Department of Biometry and Data Management Leibniz Institute for Prevention Research Epidemiology - BIPS Bremen Germany Faculty of Mathematics/Computer Science University of Bremen Bremen Germany

Prediction models are used amongst others to inform medical decisions on interventions. Typically, individuals with high risks of adverse outcomes are advised to undergo an intervention while those at low risk are advised to refrain from it. Standard prediction models do not always provide risks that are relevant to inform such decisions: e.g., an individual may be estimated to be at low risk because similar individuals in the past received an intervention which lowered their risk. Therefore, prediction models supporting decisions should target risks belonging to defined intervention strategies. Previous works on prediction under interventions assumed that the prediction model was used only at one time point to make an intervention decision. In clinical practice, intervention decisions are rarely made only once: they might be repeated, deferred and re-evaluated. This requires estimated risks under interventions that can be reconsidered at several potential decision moments. In the current work, we highlight key considerations for formulating estimands in sequential prediction under interventions that can inform such intervention decisions. We illustrate these considerations by giving examples of estimands for a case study about choosing between vaginal delivery and cesarean section for women giving birth. Our formalization of prediction tasks in a sequential, causal, and estimand context provides guidance for future studies to ensure that the right question is answered and appropriate causal estimation approaches are chosen to develop sequential prediction models that can inform intervention decisions. © 2023, CC BY.

关键词： Forecasting

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Outlier-free isogeometric discretizations for Laplace eigenvalue problems: closed-form eigenvalue and eigenvector expressions

arXiv

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arXiv 2025年

作者： Lamsahel, Noureddine Manni, Carla Ratnani, Ahmed Serra-Capizzano, Stefano Speleers, Hendrik Mohammed VI Polytechnic University The UM6P Vanguard Center Benguerir 43150 Lot Hay Moulay Rachid660 Morocco University of Littoral Côte d’Opale Laboratory of Pure and Applied Mathematics 50 Rue F. Buisson Calais62228 Cedex France University of Rome Tor Vergata Department of Mathematics Via della Ricerca Scientifica 1 Rome00133 Italy University of Insubria Department of Science and High Technology Via Valleggio 11 Como22100 Italy Uppsala University Department of Information Technology Division of Scientific Computing ITC Lägerhyddsv. 2 Hus 2 P.O. Box 337 UppsalaSE-751 05 Sweden

We derive explicit closed-form expressions for the eigenvalues and eigenvectors of the matrices resulting from isogeometric Galerkin discretizations based on outlier-free spline subspaces for the Laplace operator, under different types of homogeneous boundary conditions on bounded intervals. For optimal spline subspaces and specific reduced spline spaces, represented in terms of B-spline-like bases, we show that the corresponding mass and stiffness matrices exhibit a Toeplitz-minus-Hankel or Toeplitz-plus-Hankel structure. Such matrix structure holds for any degree p and implies that the eigenvalues are an explicitly known sampling of the spectral symbol of the Toeplitz part. Moreover, by employing tensor-product arguments, we extend the closed-form property of the eigenvalues and eigenvectors to a d-dimensional box. As a side result, we have an algebraic confirmation that the considered optimal and reduced spline spaces are indeed outlier-free. Copyright © 2025, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Quantum Circuits for Exact Unitary t-Designs and Applications to Higher-Order Randomized Benchmarking

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PRX Quantum 2021年第3期2卷 030339-030339页

作者： Yoshifumi Nakata Da Zhao Takayuki Okuda Eiichi Bannai Yasunari Suzuki Shiro Tamiya Kentaro Heya Zhiguang Yan Kun Zuo Shuhei Tamate Yutaka Tabuchi Yasunobu Nakamura Photon Science Center Graduate School of Engineering The University of Tokyo Bunkyo-ku Tokyo 113–8656 Japan JST PRESTO 4–1–8 Honcho Kawaguchi Saitama 332–0012 Japan School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 400240 China Department of Mathematics Hiroshima University 1-3-1 Kagamiyama Higashihiroshima 739-8562 Japan Faculty of Mathematics Kyushu University (emeritus) Fukuoka 819-0385 Japan Mathematics Division National Center for Theoretical Sciences National Taiwan University Taipei 10617 Taiwan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan Department of Applied Physics Graduate School of Engineering The University of Tokyo 7-3-1 Hongo Bynkyo-ku Tokyo 113-8656 Japan Research Center for Advanced Science and Technology (RCAST) The University of Tokyo Meguro-ku Tokyo 153-8904 Japan RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan

A unitary t-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general t. In this paper, we provide quantum circuits that generate exact unitary t-designs for any t on an arbitrary number of qubits. Our construction is inductive and is of practical use in small systems. We then introduce a tth-order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs. We particularly study the 2-RB in detail and show that it reveals self-adjointness of quantum noise, a metric related to the feasibility of quantum error correction (QEC). We numerically demonstrate that the 2-RB in one- and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the 2-RB. It is shown from the experiment that interactions with adjacent qubits induce the noise that may result in an obstacle toward a realization of QEC.

关键词： Quantum algorithms Quantum benchmarking Quantum gates Quantum protocols

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Leveraging randomized compiling for the QITE algorithm

arXiv

引用

arXiv 2021年

作者： Ville, Jean-Loup Morvan, Alexis Hashim, Akel Naik, Ravi K. Lu, Marie Mitchell, Bradley Kreikebaum, John-Mark O’Brien, Kevin P. Wallman, Joel J. Hincks, Ian Emerson, Joseph Smith, Ethan Younis, Ed Iancu, Costin Santiago, David I. Siddiqi, Irfan Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Inst. for Quantum Computing Dept. of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices. © 2021, CC BY.

关键词： Benchmarking

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