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arXiv 2024年

作者： Hashim, Akel Nguyen, Long B. Goss, Noah Marinelli, Brian Naik, Ravi K. Chistolini, Trevor Hines, Jordan Marceaux, J.P. Kim, Yosep Gokhale, Pranav Tomesh, Teague Chen, Senrui Jiang, Liang Ferracin, Samuele Rudinger, Kenneth Proctor, Timothy Young, Kevin C. Blume-Kohout, Robin Siddiqi, Irfan Department of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Math and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Quantum Performance Laboratory Sandia National Laboratories Albuquerque NM 87185 and LivermoreCA94550 United States Graduate Group in Applied Science and Technology University of California at Berkeley BerkeleyCA94720 United States Department of Physics Korea University Seoul02841 Korea Republic of Infleqtion ChicagoIL60604 United States Pritzker School of Molecular Engineering University of Chicago IL60637 United States Keysight Technologies Canada KanataONK2K 2W5 Canada Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States

Rapid progress in quantum technology has transformed quantum computing and quantum information science from theoretical possibilities into tangible engineering challenges. Breakthroughs in quantum algorithms, quantum simulations, and quantum error correction are bringing useful quantum computation closer to fruition. These remarkable achievements have been facilitated by advances in quantum characterization, verification, and validation (QCVV). QCVV methods and protocols enable scientists and engineers to scrutinize, understand, and enhance the performance of quantum information-processing devices. In this Tutorial, we review the fundamental principles underpinning QCVV, and introduce a diverse array of QCVV tools used by quantum researchers. We define and explain QCVV’s core models and concepts — quantum states, measurements, and processes — and illustrate how these building blocks are leveraged to examine a target system or operation. We survey and introduce protocols ranging from simple qubit characterization to advanced benchmarking methods. Along the way, we provide illustrated examples and detailed descriptions of the protocols, highlight the advantages and disadvantages of each, and discuss their potential scalability to future large-scale quantum computers. This Tutorial serves as a guidebook for researchers unfamiliar with the benchmarking and characterization of quantum computers, and also as a detailed reference for experienced practitioners. Copyright © 2024, The Authors. All rights reserved.

关键词： Error correction

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Symmetrically Threaded SQUIDs As Next Generation Kerr-cat Qubits

arXiv

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arXiv 2024年

作者： Bhandari, Bibek Huang, Irwin Hajr, Ahmed Yanik, Kagan Qing, Bingcheng Wang, Ke Santiago, David I. Dressel, Justin Siddiqi, Irfan Jordan, Andrew N. Institute for Quantum Studies Chapman University OrangeCA92866 United States Department of Physics and Astronomy University of Rochester RochesterNY14627 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Graduate Group in Applied Science and Technology University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory Berkeley BerkeleyCA94720 United States Schmid College of Science and Technology Chapman University OrangeCA92866 United States Chapman University OrangeCA92866 United States

Kerr-cat qubits are bosonic qubits with autonomous protection against bit-flips. They have been studied widely using driven Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) oscillators. We theoretically investigate an alternate circuit for the Kerr-cat qubit, namely Symmetrically Threaded SQUIDs (STS). We perform the circuit analysis and derive the Gorini-Kossakowski-Sudarshan-Lindblad (GKLS) master equation for the Kerr-cat qubit attached to a thermal environment. We find that the lifetime time of the coherent states (Tα) of the Kerr-cat qubit is the same in both the STS and SNAIL circuits for weak Kerr nonlinearity. However, the STS Kerr-cat qubits have the additional benefit of being resistant against higher order photon dissipation effects, resulting in significantly longer Tα even with stronger Kerr nonlinearity on the order of 10 MHz. We also examine the effects of strong flux driving and asymmetric Josephson junctions on Tα. Unlike the SNAIL design, we find a dip in Tα of the STS Kerr-cat qubit for weak two-photon drive. However, we show that the dip can be mitigated by applying a suitable drive-dependent detuning. With the proposed design and considering a cat size of 10 photons, we predict Tα of the order of tens of milliseconds even in the presence of multi-photon heating and dephasing effects. The robustness of the STS Kerr-cat qubit makes it a promising component for fault-tolerant quantum processors. © 2024, CC BY-NC-ND.

关键词： Photons

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Social distancing and COVID-19: Randomization inference for a structured dose-response relationship

arXiv

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arXiv 2020年

作者： Zhang, Bo Heng, Siyu Ye, Ting Small, Dylan S. Department of Statistics The Wharton School University of Pennsylvania Graduate Group in Applied Mathematics and Computational Science School of Arts and Sciences University of Pennsylvania

Social distancing is widely acknowledged as an effective public health policy combating the novel coronavirus. But extreme forms of social distancing like isolation and quarantine have costs and it is not clear how much social distancing is needed to achieve public health effects. In this article, we develop a design-based framework to test the causal null hypothesis and make inference about the dose-response relationship between reduction in social mobility and COVID-19 related public health outcomes. We first discuss how to embed observational data with a time-independent, continuous treatment dose into an approximate randomized experiment, and develop a randomization-based procedure that tests if a structured dose-response relationship fits the data. We then generalize the design and testing procedure to accommodate a time-dependent treatment dose in a longitudinal setting. Finally, we apply the proposed design and testing procedures to investigate the effect of social distancing during the phased reopening in the United States on public health outcomes using data compiled from sources including Unacast™, the United States Census Bureau, and the County Health Rankings and Roadmaps Program. We rejected a primary analysis null hypothesis that stated the social distancing from April 27, 2020, to June 28, 2020, had no effect on the COVID-19-related death toll from June 29, 2020, to August 2, 2020 (p-value © 2020, CC0.

关键词： Random processes

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Leveraging Error-Prone Algorithm-Derived Phenotypes: Enhancing Association Studies for Risk Factors in Ehr Data

SSRN

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SSRN 2024年

作者： Lu, Yiwen Tong, Jiayi Chubak, Jessica Lumley, Thomas Hubbard, Rebecca A. Xu, Hua Chen, Yong Department of Biostatistics Epidemiology and Informatics Perelman School of Medicine University of Pennsylvania PhiladelphiaPA United States The Graduate Group in Applied Mathematics and Computational Science School of Arts and Sciences University of Pennsylvania PhiladelphiaPA United States Kaiser Permanente Washington Health Research Institute SeattleWA United States Department of Statistics Faculty of Science University of Auckland Auckland New Zealand Department of Biostatistics Epidemiology and Informatics Perelman School of Medicine University of Pennsylvania PhiladelphiaPA United States PhiladelphiaPA United States Department of Biomedical Informatics and Data Science Yale University New HavenCT United States Leonard Davis Institute of Health Economics PhiladelphiaPA United States PhiladelphiaPA United States

ObjectivesIt has become increasingly common for multiple computable phenotypes from electronic health records (EHR) to be developed for a given phenotype. However, EHR-based association studies often focus on a single phenotype. In this paper, we develop a method aiming to simultaneously make use of multiple EHR-derived phenotypes for reduction of bias due to phenotyping error and improved efficiency of phenotype/exposure *** and MethodsThe proposed method combines multiple algorithm-derived phenotypes with a small set of validated outcomes to reduce bias and improve estimation accuracy and efficiency. The performance of our method was evaluated through simulation studies and real-world application to an analysis of colon cancer recurrence using EHR data from Kaiser Permanente *** settings where there was no single surrogate performing uniformly better than all others in terms of both sensitivity and specificity, our method achieved substantial bias reduction compared to using a single algorithm-derived phenotype. Our method also led to higher estimation efficiency by up to 30% compared to an estimator that used only one algorithm-derived *** studies and application to real-world data demonstrated the effectiveness of our method in integrating multiple phenotypes, thereby enhancing bias reduction, statistical accuracy and *** method combines information across multiple surrogates using a statistically efficient seemingly unrelated regression framework. Our method provides a robust alternative to single-surrogate-based bias correction, especially in contexts lacking information on which surrogate is superior. © 2024, The Authors. All rights reserved.

关键词： Efficiency

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Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity

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Physical Review D 2021年第6期104卷 063517-063517页

作者： Daris Samart Bhuddhanubhap Silasan Phongpichit Channuie Khon Kaen Particle Physics and Cosmology Theory Group (KKPaCT) Department of Physics Faculty of Science Khon Kaen University 123 Mitraphap road Khon Kaen 40002 Thailand College of Graduate Studies Walailak University Thasala Nakhon Si Thammarat 80160 Thailand School of Science Walailak University Thasala Nakhon Si Thammarat 80160 Thailand Research Group in Applied Computational and Theoretical Science (ACTS) Walailak University Thasala Nakhon Si Thammarat 80160 Thailand

In this work, we investigate the dynamics of the interacting dark energy and dark matter in viable models of f(R) gravity by using a standard framework of dynamical system analysis. A simple form of the interacting dark energy Q=3αHρm is used to study three viable models of f(R) gravity which are consistent with local gravity constraints and satisfying conditions for the cosmological viability. As a result, we find that the fixed points are slightly modified from those obtained in the standard noninteracting analysis of f(R) gravity proposed so far in the literature. In our models of adding this interaction, we find that the dynamical profiles of the Universe in the viable f(R) dark energy models are modified by the interaction term as well as their relevant model parameters. Moreover, our results yield the correct cosmological evolution with additional constraint parameter, α, from the interacting dark energy.

关键词： Alternative gravity theories Cosmological parameters Fluids & classical fields in curved spacetime

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Deep learning with Gaussian differential privacy

arXiv

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arXiv 2019年

作者： Bu, Zhiqi Dong, Jinshuo Long, Qi Su, Weijie J. Graduate Group in Applied Mathematics and Computational Science Graduate Group in Applied Mathematics and Computational Science Department of Biostatistics Epidemiology and Informatics Department of Statistics

Deep learning models are often trained on datasets that contain sensitive information such as individuals' shopping transactions, personal contacts, and medical records. An increasingly important line of work therefore has sought to train neural networks subject to privacy constraints that are specified by differential privacy or its divergence-based relaxations. These privacy definitions, however, have weaknesses in handling certain important primitives (composition and subsampling), thereby giving loose or complicated privacy analyses of training neural networks. In this paper, we consider a recently proposed privacy definition termed f-differential privacy [17] for a refined privacy analysis of training neural networks. Leveraging the appealing properties of f-differential privacy in handling composition and subsampling, this paper derives analytically tractable expressions for the privacy guarantees of both stochastic gradient descent and Adam used in training deep neural networks, without the need of developing sophisticated techniques as [3] did. Our results demonstrate that the f-differential privacy framework allows for a new privacy analysis that improves on the prior analysis [3], which in turn suggests tuning certain parameters of neural networks for a better prediction accuracy without violating the privacy budget. These theoretically derived improvements are confirmed by our experiments in a range of tasks in image classification, text classification, and recommender systems. Copyright © 2019, The Authors. All rights reserved.

关键词： Text processing

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Brilliant Challenges Optimization Problem Submission Contest Final Report

arXiv

引用

arXiv 2021年

作者： Badura, Jan Laskowski, Artur Antczak, Maciej Blazewicz, Jacek Pawlak, Grzegorz Pesch, Erwin Villmann, Thomas Wasik, Szymon Institute of Computing Science Poznan University of Technology European Center for Bioinformatics and Genomics Poznan University of Technology Institute of Bioorganic Chemistry Polish Academy of Sciences Center of Advanced Studies in Management HHL Leipzig Graduate School of Management Department of Management Information Science University of Siegen Computational Intelligence Group University of Applied Sciences Mittweida

This paper concludes the Brilliant Challenges contest. Participants had to design interesting optimization problems and publish them using the *** platform. It was the first widely-advertised contest in the area of operational research where the objective was to submit the problem definition instead of the algorithmic solutions. Thus, it is a crucial contribution to Open science and the application of crowdsourcing methodology to solve discrete optimization problems. The paper briefly describes submitted problems, presents the winners, and discusses the contest’s achievements and shortcomings. Finally, we define guidelines supporting the organization of contests of similar type in the future. © 2021, CC BY.

关键词： Optimization

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A Local Polyak-Lojasiewicz and Descent Lemma of Gradient Descent For Overparametrized Linear Models

arXiv

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arXiv 2025年

作者： Xu, Ziqing Min, Hancheng Tarmoun, Salma Mallada, Enrique Vidal, René Department of Statistics and Data Science the Wharton School University of Pennsylvania United States University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Electrical and Computer Engineering Johns Hopkins University United States Department of Electrical and Systems Engineering Department of Radiology University of Pennsylvania United States

Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (large, spectral, balanced). Recent efforts to relax these assumptions focus on two-layer linear networks trained with the squared loss. In this work, we derive a linear convergence rate for training two-layer linear neural networks with GD for general losses and under relaxed assumptions on the step size, width, and initialization. A key challenge in deriving this result is that classical ingredients for deriving convergence rates for nonconvex problems, such as the Polyak-Lojasiewicz (PL) condition and Descent Lemma, do not hold globally for overparameterized neural networks. Here, we prove that these two conditions hold locally with local constants that depend on the weights. Then, we provide bounds on these local constants, which depend on the initialization of the weights, the current loss, and the global PL and smoothness constants of the non-overparameterized model. Based on these bounds, we derive a linear convergence rate for GD. Our convergence analysis not only improves upon prior results but also suggests a better choice for the step size, as verified through our numerical experiments. © 2025, CC BY.

关键词： Dynamic models

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Optimized SWAP networks with equivalent circuit averaging for QAOA

引用

Physical Review Research 2022年第3期4卷 033028-033028页

作者： Akel Hashim Rich Rines Victory Omole Ravi K. Naik John Mark Kreikebaum David I. Santiago Frederic T. Chong Irfan Siddiqi Pranav Gokhale 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 Super.tech a division of ColdQuanta Chicago Illinois 60615 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA University of Chicago Chicago Illinois 60637 USA

The SWAP network is a qubit routing sequence that can be used to efficiently execute the Quantum Approximate Optimization Algorithm (QAOA). Even with a minimally connected topology on an n-qubit processor, this routing sequence enables O(n2) operations to execute in O(n) steps. In this work, we optimize the execution of SWAP networks for QAOA through two techniques. First, we take advantage of an overcomplete set of native hardware operations [including 150-ns controlled-π2 phase gates with up to 99.67(1)% fidelity] to decompose the relevant quantum gates and SWAP networks in a manner which minimizes circuit depth and maximizes gate cancellation. Second, we introduce equivalent circuit averaging, which randomizes over degrees of freedom in the quantum circuit compilation to reduce the impact of systematic coherent errors. Our techniques are experimentally validated at the Advanced Quantum Testbed through the execution of QAOA circuits for finding the ground state of two- and four-node Sherrington-Kirkpatrick spin-glass models with various randomly sampled parameters. We observe a ∼60% average reduction in error (total variation distance) for QAOA of depth p=1 on four transmon qubits on a superconducting quantum processor.

关键词： Quantum algorithms Quantum benchmarking Quantum gates

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UNDERSTANDING AND MITIGATING GRADIENT PATHOLOGIES IN PHYSICS-INFORMED NEURAL NETWORKS

arXiv

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arXiv 2020年

作者： Wang, Sifan Teng, Yujun Perdikaris, Paris Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA 19104 United States Department of Mechanichal Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104 United States

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://***/PredictiveIntelligenceLab/ GradientPathologiesPINNs. Copyright © 2020, The Authors. All rights reserved.

关键词： Network architecture

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