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Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators

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Physical Review Research 2024年第4期6卷 043245-043245页

作者： Mary Kreidel Xuanjing Chu Jesse Balgley Abhinandan Antony Nishchhal Verma Julian Ingham Leonardo Ranzani Raquel Queiroz Robert M. Westervelt School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Mechanical Engineering Columbia University New York New York 10027 USA Department of Physics Columbia University New York New York 10027 USA RTX BBN Technologies Quantum Engineering and Computing Group Cambridge Massachusetts 02138 USA Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA

The discovery of van der Waals superconductors in recent years has generated a lot of excitement for their potentially novel pairing mechanisms. However, their typical atomic-scale thickness and micrometer-scale lateral dimensions impose severe challenges to investigations of pairing symmetry by conventional methods. We demonstrate an improved technique that employs high-quality-factor superconducting resonators to measure the kinetic inductance—up to one part per million—and loss of a van der Waals superconductor. We analyze the equivalent circuit model to extract the kinetic inductance, superfluid stiffness, penetration depth, and ratio of imaginary and real parts of the complex conductivity. We validate the technique by measuring aluminum and finding excellent agreement in both the zero-temperature superconducting gap as well as the complex conductivity data when compared with BCS theory. We then demonstrate the utility of the technique by measuring the kinetic inductance of multilayered niobium diselenide and discuss the limits to the accuracy of our technique when the transition temperature of the sample, NbSe2 at 7.06 K, approaches our Nb probe resonator at 8.59 K. Our method will be useful for practitioners in the growing fields of superconducting physics, materials science, and quantum sensing, as a means of characterizing superconducting circuit components and studying pairing mechanisms of the novel superconducting states which arise in layered two-dimensional materials and heterostructures.

关键词： Quantum circuits Superconducting order parameter Superconductivity 2-dimensional systems Van der Waals systems Methods in superconductivity Microwave techniques

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Heisenberg and Heisenberg-like representations via Hilbert-space-bundle geometry in the non-Hermitian regime

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Physical Review A 2025年第5期111卷 052213-052213页

作者： Chia-Yi Ju Adam Miranowicz Jacob Barnett Guang-Yin Chen Franco Nori Department of Physics National Sun Yat-sen University Kaohsiung 80424 Taiwan Center for Theoretical and Computational Physics National Sun Yat-sen University Kaohsiung 80424 Taiwan Physics Division National Center for Theoretical Sciences Taipei 106319 Taiwan Institute of Spintronics and Quantum Information Faculty of Physics and Astronomy Adam Mickiewicz University 61-614 Poznań Poland Center for Quantum Computing RIKEN Wakoshi Saitama 351-0198 Japan Basque Center for Applied Mathematics Alameda de Mazarredo 14 48009 Bilbao Bizkaia Spain Department of Physics National Chung Hsing University Taichung 40227 Taiwan Department of Physics University of Michigan Ann Arbor Michigan 48109-1040 USA

The equivalence between the Schrödinger and Heisenberg representations is a cornerstone of quantum mechanics. However, this relationship remains unclear in the non-Hermitian regime, particularly when the Hamiltonian is time dependent. In this paper, we address this gap by establishing the connection between the two representations, incorporating the metric of the Hilbert space bundle. We not only demonstrate the consistency between the Schrödinger and Heisenberg representations but also present a Heisenberg-like representation grounded in the generalized vielbein formalism, which provides a clear and intuitive geometric interpretation. Unlike the standard Heisenberg representation, where the metric of the Hilbert space is encoded solely in the dual states, the Heisenberg-like representation distributes the metric information between both the states and the dual states. Despite this distinction, it retains the same Heisenberg equation of motion for operators. Within this formalism, the Hamiltonian is replaced by a Hermitian counterpart, while the “non-Hermiticity” is transferred to the operators. Moreover, this approach extends to regimes with a dynamical metric (beyond the pseudo-Hermitian framework) and to systems governed by time-dependent Hamiltonians.

关键词： Hilbert spaces

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On Controllability of Driftless Control System on Symmetric Spaces

arXiv

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arXiv 2021年

作者： Tiwari, Archana Padhan, R.N. Pati, Kishor Chandra Department of Mathematics National Institute of Technology Odisha Rourkela769008 India Center for Applied Mathematics and Computing ITER Sikhsha’O’ Anusandhan BBSR Odisha 751030 India

Symmetric spaces arise in wide variety of problems in mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type x = Pmi=1 uifi(x) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles. Copyright © 2021, The Authors. All rights reserved.

关键词： Controllability

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Dense Outputs from Quantum Simulations

SSRN

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SSRN 2023年

作者： Liu, Jin-Peng Lin, Lin Department of Mathematics University of California Berkeley United States Simons Institute for the Theory of Computing University of California Berkeley United States Center for Theoretical Physics Massachusetts Institute of Technology Cambridge United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley Berkeley United States

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $\epsilon$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/\epsilon)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. © 2023, The Authors. All rights reserved.

关键词： Linearization

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Dense outputs from quantum simulations

arXiv

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arXiv 2023年

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time T and error tolerance ǫ. Our results demonstrate that the linearization approach can nearly achieve optimal complexity O(T/ǫ) for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. Copyright © 2023, The Authors. All rights reserved.

关键词： Linearization

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Kilometer-Scale E3SM Land Model Simulation over North America

arXiv

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arXiv 2025年

作者： Wang, Dali Wang, Chen Cao, Qinglei Schwartz, Peter Yuan, Fengming Krishna, Jayesh Wu, Danqing Ricciuto, Danial Thornton, Peter Kao, Shih-Chieh Thornton, Michele Mohror, Kathryn Environmental Sciences Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States Department of Computer Science Saint Louis University Saint LouisMO United States Mathematics and Computer Sciences Argonne National Laboratory ArgonneIL United States

The development of a kilometer-scale E3SM Land Model (km-scale ELM) is an integral part of the E3SM project, which seeks to advance energy-related Earth system science research with state-of-the-art modeling and simulation capabilities on exascale computing systems. Through the utilization of high-fidelity data products, such as atmospheric forcing and soil properties, the km-scale ELM plays a critical role in accurately modeling geographical characteristics and extreme weather occurrences. The model is vital for enhancing our comprehension and prediction of climate patterns, as well as their effects on ecosystems and human activities. This study showcases the first set of full-capability, km-scale ELM simulations over various computational domains, including simulations encompassing 21.6 million land gridcells, reflecting approximately 21.5 million square kilometers of North America at a 1 km × 1 km resolution. We present the largest km-scale ELM simulation using up to 100,800 CPU cores across 2,400 nodes. This continental-scale simulation is 300 times larger than any previous studies, and the computational resources used are about 400 times larger than those used in prior efforts. Both strong and weak scaling tests have been conducted, revealing exceptional performance efficiency and resource utilization. The km-scale ELM uses the common E3SM modeling infrastructure and a general data toolkit known as KiloCraft. Consequently, it can be readily adapted for both fully-coupled E3SM simulations and data-driven simulations over specific areas, ranging from a single gridcell to the entire North America. © 2025, CC BY.

关键词： Digital elevation model

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GBO: A Multi-Granularity Optimization Algorithm via Granular-ball for Continuous Problems

arXiv

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arXiv 2023年

作者： Xia, Shuyin Lin, Xinyu Wang, Guan Chen, De-Gang Zhao, Sen Wang, Guoyin Liang, Jing Chongqing Key Laboratory of Computational Intelligence China Key Laboratory of Big Data Intelligent Computing China Chongqing University of Posts and Telecommunications Chongqing China Chongqing Normal University China National Center for Applied Mathematics in Chongging Chongging Normal University Chongging401331 China Zhengzhou University China

Optimization problems aim to find the optimal solution, which is becoming increasingly complex and difficult to solve. Traditional evolutionary optimization methods always overlook the granular characteristics of solution space. In the real scenario of numerous optimizations, the solution space is typically partitioned into sub-regions characterized by varying degree distributions. These sub-regions present different granularity characteristics at search potential and difficulty. Considering the granular characteristics of the solution space, the number of coarse-grained regions is smaller than the number of points, so the calculation is more efficient. On the other hand, coarse-grained characteristics are not easily affected by fine-grained sample points, so the calculation is more robust. To this end, this paper proposes a new multi-granularity evolutionary optimization method, namely the Granular-ball Optimization (GBO) algorithm, which characterizes and searches the solution space from coarse to fine. Specifically, using granular-balls instead of traditional points for optimization increases the diversity and robustness of the random search process. At the same time, the search range in different iteration processes is limited by the radius of granular-balls, covering the solution space from large to small. The mechanism of granular-ball splitting is applied to continuously split and evolve the large granular-balls into smaller ones for refining the solution space. Extensive experiments on commonly used benchmarks have shown that GBO outperforms popular and advanced evolutionary algorithms. The code can be found in the supporting materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Optimization algorithms

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Heterogeneous data analysis of hypertrophic cardiomyopathy to prioritize important genes

Heterogeneous data analysis of hypertrophic cardiomyopathy t...

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International Computer Science and Engineering Conference (ICSEC)

作者： Panisa Janyasupab Apichat Suratanee Kitiporn Plaimas Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand Department of Mathematics Faculty of Applied Science King Mongkut’s University of Technology North Bangkok Bangkok Thailand Department of Mathematics and Computer Science Faculty of Science Advance Virtual and Intelligent Computing (AVIC) Center Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9781665462730

Hypertrophic cardiomyopathy (HCM) is a cardiovascular disease that is often caused by abnormal genes in the heart muscle. The identification of HCM-related genes is one of the crucial tasks to prevent and treat the patient. Gene expression analysis is a direct approach to screen for a gene with a higher or lower expression level in the HCM cell than in the normal cell. Microarray and RNA-Seq technology are used for measuring transcription levels. Both techniques have different advantages to obtain gene expression data. The integration of microarray and RNA-Seq data has already been effectively used to identify disease biomarkers. The ranking method is an interesting technique and is mostly used for ranking players or teams in sports. Each method has different strengths and can be appropriately applied to integrate various data and used to prioritize the importance genes. In this work, six ranking techniques to integrate microarray and RNA-Seq data were applied to prioritize the HCM-related genes. The performance reveals that the ranking method is also a well-suited technique in this task, and it turns out that the PageRank technique yields the best performance.

关键词： Heart Computer science Data analysis Computational modeling Muscles Biomarkers Gene expression

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Boosting Earth System Model Outputs And Saving PetaBytes in their Storage Using Exascale Climate Emulators

arXiv

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arXiv 2024年

作者： Abdulah, Sameh Baker, Allison H. Bosilca, George Cao, Qinglei Castruccio, Stefano Genton, Marc G. Keyes, David E. Khalid, Zubair Ltaief, Hatem Song, Yan Stenchikov, Georgiy L. Sun, Ying Extreme Computing & Statistics & Earth Science King Abdullah University of Science and Technology KSA Saudi Arabia Computational and Information Sciences Lab NSF National Center for Atmospheric Research United States NVIDIA United States Department of Computer Science Saint Louis University United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

We present the design and scalable implementation of an exascale climate emulator for addressing the escalating computational and storage requirements of high-resolution Earth System Model simulations. We utilize the spherical harmonic transform to stochastically model spatio-temporal variations in climate data. This provides tunable spatio-temporal resolution and significantly improves the fidelity and granularity of climate emulation, achieving an ultra-high spatial resolution of 0.034◦ (∼3.5 km) in space. Our emulator, trained on 318 billion hourly temperature data points from a 35-year and 31 billion daily data points from an 83-year global simulation ensemble, generates statistically consistent climate emulations. We extend linear solver software to mixed-precision arithmetic GPUs, applying different precisions within a single solver to adapt to different correlation strengths. The PaRSEC runtime system supports efficient parallel matrix operations by optimizing the dynamic balance between computation, communication, and memory requirements. Our BLAS3-rich code is optimized for systems equipped with four different families and generations of GPUs, scaling well to achieve 0.976 EFlop/s on 9,025 nodes (36,100 AMD MI250X multi-chip module (MCM) GPUs) of Frontier (nearly full system), 0.739 EFlop/s on 1,936 nodes (7,744 Grace-Hopper Superchips (GH200)) of Alps, 0.243 EFlop/s on 1,024 nodes (4,096 A100 GPUs) of Leonardo, and 0.375 EFlop/s on 3,072 nodes (18,432 V100 GPUs) of Summit. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing

arXiv

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arXiv 2024年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Bu, Lijing Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China College of Mathematical Medicine Zhejiang Normal University Jinhua321004 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models, which may not effectively capture the imaging mechanisms of remote sensing images. Furthermore, many RS image restoration approaches that use deep learning are often criticized for their lacks of architecture transparency and model interpretability. To address these problems, we propose a novel progressive restoration network for high-order degradation imaging (HDI-PRNet), to progressively restore different image degradation. HDI-PRNet is developed based on the theoretical framework of degradation imaging, offering the benefit of mathematical interpretability within the unfolding network. The framework is composed of three main components: a module for image denoising that relies on proximal mapping prior learning, a module for image deblurring that integrates Neumann series expansion with dual-domain degradation learning, and a module for super-resolution. Extensive experiments demonstrate that our method achieves superior performance on both synthetic and real remote sensing images. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

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