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On the Schrödingerization method for linear non-unitary dynamics with optimal dependence on matrix queries

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arXiv 2025年

作者： Jin, Shi Liu, Nana Ma, Chuwen Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

The Schrödingerization method converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations with unitary evolution. It does so via the so-called warped phase transformation that maps the original equation into a Schrödinger-type equation in one higher dimension [1,2]. We show that by employing a smooth initialization of the warped phase transform [3], Schrödingerization can in fact achieve optimal scaling in matrix queries. This paper presents the detailed implementation of three smooth initializations for the Schrödingerization method: (a) the cut-off function, (b) the higher-order polynomial interpolation, and (c) the Fourier transform methods, that achieve optimality for (a) and near-optimality for (b) and (c). A detailed analysis of key parameters affecting time complexity is conducted. Copyright © 2025, The Authors. All rights reserved.

关键词： Ordinary differential equations

Quantum circuits for the heat equation with physical boundary conditions via Schrödingerization

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Journal of computational Physics 2025年 538卷

作者： Shi Jin Nana Liu Yue Yu School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai 200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai 200240 China School of Mathematics and Computational Science Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 Hunan China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not directly suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerization method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerization techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [1] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle.

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Disconnection-mediated migration of interfaces in microstructures: I. Continuum model

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arXiv 2021年

作者： Han, Jian Srolovitz, David J. Salvalaglio, Marco Department of Materials Science and Engineering City University of Hong Kong Hong Kong Hong Kong Department of Mechanical Engineering University of Hong Kong Pokfulam Road Hong Kong Hong Kong Hong Kong Institute for Advanced Study City University of Hong Kong Hong Kong Hong Kong Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany

A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion;hence, the establishment of rigorous interface equations of motion is a universal goal of materials science. We present a new model for the motion of arbitrarily curved interfaces that respects the underlying crystallography of the two phases/domains meeting at the interface and is consistent with microscopic mechanisms of interface motion;i.e., disconnection migration (line defects in the interface with step and dislocation character). We derive the equation of motion for interface migration under the influence of a wide range of driving forces. In Part II of this paper [Salvalaglio, Han and Srolovitz, 2021], we implement the interface model and the equation of motion proposed in this paper in a diffuse interface simulation approach for complex morphology and microstructure evolution. Copyright © 2021, The Authors. All rights reserved.

关键词： Equations of motion

Schrödingerization based quantum algorithms for the fractional Poisson equation

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arXiv 2025年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the d-dimensional fractional equation is reformulated as a local partial differential equation in d + 1 dimensions. We propose a quantum algorithm for the finite element discretization of this local problem, by capturing the steady-state of the corresponding differential equations using the Schrödingerization approach from [29, 39, 40]. The Schrödingerization technique transforms general linear partial and ordinary differential equations into Schrödinger-type systems, making them suitable for quantum simulation. This is achieved through the warped phase transformation, which maps the equation into a higher-dimensional space. We provide detailed implementations of the method and conduct a comprehensive complexity analysis, which can show up to exponential advantage – with respect to the inverse of the mesh size in high dimensions – compared to its classical counterpart. Specifically, while the classical method requires Oe(d1/233d/2h−d−2) operations, the quantum counterpart requires Oe(d33d/2h−2.5) queries to the block-encoding input models, with the quantum complexity being independent of the dimension d in terms of the inverse mesh size h−1. Numerical experiments are conducted to verify the validity of our formulation. © 2025, CC BY-NC-ND.

关键词： Poisson equation

The application of proximal visible and near-infrared spectroscopy to estimate soil organic matter on the Triffa Plain of Morocco

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International Soil and Water Conservation Research 2020年第2期8卷 195-204页

作者： Ayoub Lazaar Abdul Mounem Mouazen Kamal EL Hammouti Michael Fullen Biswajeet Pradhan Muhammad Sohail Memon Karim Andich Abdelilah Monir Laboratory of Applied Geosciences Department of GeologyFaculty of ScienceMohammed First UniversityOujdaMorocco Division of Mechatronics Biostatistics and Sensors(MeBioS)Faculty of Bioscience EngineeringKasteelpark Arenberg 30B-3001 HeverleeBelgium Faculty of Science and Engineering University of WolverhamptonWolverhamptonWV11LYUnited Kingdom Center for Advanced Modelling and Geospatial Information Systems(CAMGIS) Faculty of Engineering and Information TechnologyUniversity of Technology SydneySydney2007NSWAustralia Faculty of Agricultural Engineering Sindh Agriculture UniversityTandojam70060Pakistan Laboratory of Applied Geomatics and Soil Science National Institute of Agronomic Research(INRA)OujdaMorocco Department of Mathematics EDP and Scientific Computing TeamMoulay Ismail UniversityMéknesMorocco

Soil organic matter (SOM) is a fundamental soil constituent. The estimation of this parameter in the laboratory using the classical method is complex time-consuming and requires the use of chemical re-agents. The objectives of this study were to assess the accuracy of two laboratory measurement setups of the VIS-NIR spectroscopy in estimating SOM content and determine the important spectral bands in the SOM estimation model. A total of 115 soil samples were collected from the non-root zone (0-20 cm) of soil in the study area of the Triffa Plain and then analysed for SOM in the laboratory by the Walkley-Black method. The reflectance spectra of soil samples were measured by two protocols, Contact Probe (CP) and Pistol Grip (PG)) of the ASD spectroradiometer (350-2500 nm) in the laboratory. Partial least squares regression (PLSR) was used to develop the prediction models. The results of coefficient of determination (R2) and the root mean square error (RMSE) showed that the pistol grip offers reasonable accuracy with an R2=0.93 and RMSE=0.13 compared to the contact probe protocol with an R2=0.85 and RMSE = 0.19. The near-Infrared range were more accurate than those in the visible range for pre-dicting SOM using the both setups (CP and PG). The significant wavelengths contributing to the pre-diction of SOM for (PG) setup were at:424, 597, 1432, 1484, 1830,1920, 2200, 2357 and 2430 nm, while were at 433, 587, 1380, 1431, 1929, 2200 and 2345 nm for (CP) setup.

关键词： Soil organic matter VIS-NIR spectroscopy Reflectance spectra SOM estimation SOM analysis

Fitness dependent optimizer with neural networks for COVID-19 patients

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Computer Methods and Programs in Biomedicine Update 2023年 3卷 100090页

作者： Abdulkhaleq, Maryam T. Rashid, Tarik A. Hassan, Bryar A. Alsadoon, Abeer Bacanin, Nebojsa Chhabra, Amit Vimal, S. Department of Computer Science and Engineering University of Kurdistan Hewler KRI Iraq Kurdistan Institution for Strategic Studies and Scientific Research Sulaimani KRI Iraq Department of Computer Networks Technical College of Informatics Sulaimani Polytechnic University Sulaimani KRI Iraq School of Computing and Mathematics Charles Sturt University Sydney Australia Information Technology Department Asia Pacific International College (APIC) Sydney Australia Singidunum University Danijelova 32 Belgrade 11000 Serbia Department of Computer Engineering and Technology Guru Nanak Dev University Amritsar India Dept of CSE Ramco Institute of Technology Tamilnadu Rajapalayam India

The Coronavirus, known as COVID-19, which appeared in 2019 in China, has significantly affected the global health and become a huge burden on health institutions all over the world. These effects are continuing today. One strategy for limiting the virus's transmission is to have an early diagnosis of suspected cases and take appropriate measures before the disease spreads further. This work aims to diagnose and show the probability of getting infected by the disease according to textual clinical data. In this work, we used five machine learning techniques (GWO_MLP, GWO_CMLP, MGWO_MLP, FDO_MLP, FDO_CMLP) all of which aim to classify Covid-19 patients into two categories (Positive and Negative). Experiments showed promising results for all used models. The applied methods showed very similar performance, typically in terms of accuracy. However, in each tested dataset, FDO_MLP and FDO_CMLP produced the best results with 100% accuracy. The other models' results varied from one experiment to the other. It is concluded that the models on which the FDO algorithm was used as a learning algorithm had the possibility of obtaining higher accuracy. However, it is found that FDO has the longest runtime compared to the other algorithms. The link to the Covid 19 models is found here: https://***/Tarik4Rashid4/covid19models © 2022

关键词： COVID 19 FDO Fitness dependent optimizer Machine learning Swarm intelligence

Lattice construction C∗ from self-dual codes

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arXiv 2020年

作者： Bollauf, Maiara F. Costa, Sueli I. R. Zamir, Ram Institute of Mathematics Statistic and Scientific Computing University of Campinas São Paulo13083-859 Brazil Deptartment Electrical Engineering-Systems Tel Aviv University Tel Aviv Israel

Construction C∗ was recently introduced as a generalization of the multilevel Construction C (or Forney's code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea of this paper is to present a 3-level lattice Construction C∗ scheme that admits an efficient nearestneighborhood decoding. In order to achieve this objective, we choose coupled codes for levels 1 and 3, and set the second level code C2 as an independent linear binary self-dual code, which is known to have a rich mathematical structure among families of linear codes. Our main result states a necessary and sufficient condition for this construction to generate a lattice. We then present examples of efficient lattices and also non-lattice constellations with good packing properties. Copyright © 2020, The Authors. All rights reserved.

关键词： C (programming language)

The generalized covering radii of linear codes

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arXiv 2020年

作者： Elimelech, Dor Firer, Marcelo Schwartz, Moshe School of Electrical and Computer Engineering Ben-Gurion University of the Negev Beer Sheva8410501 Israel Institute of Mathematics Statistics and Scientific Computing University of Campinas Campinas13083-859 Brazil

Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes – the generalized covering radius. The generalized covering-radius hierarchy of a linear code characterizes the trade-off between storage amount, latency, and access complexity, in such database systems. Several equivalent definitions are provided, showing this as a combinatorial, geometric, and algebraic notion. We derive bounds on the code parameters in relation with the generalized covering radii, study the effect of simple code operations, and describe a connection with generalized Hamming weights. Copyright © 2020, The Authors. All rights reserved.

关键词： Economic and social effects

A field guide to cultivating computational biology

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arXiv 2021年

作者： Carpenter, Anne E. Greene, Casey S. Carninci, Piero Carvalho, Benilton S De Hoon, Michiel Finley, Stacey Lê Cao, Kim-Anh Lee, Jerry S.H. Marchionni, Luigi Sindi, Suzanne S. Theis, Fabian J. Way, Gregory P. Yang, Jean Y.H. Fertig, Elana J. Imaging Platform Broad Institute of Mit and Harvard CambridgeMA United States Center for Health Ai University of Colorado School of Medicine AuroraCO United States Human Technopole Via Belgioioso 171 Milano MI20157 Italy Department of Statistics Institute of MathematicsStatistics and Scientific Computing University of Campinas Campinas Brazil Riken Center for Integrative Medical Sciences Yokohama Kanagawa Japan Department of Biomedical Engineering Quantitative and Computational Biology Chemical Engineering & Materials Science University of Southern California United States Melbourne Integrative Genomics School of Mathematics and Statistics University of Melbourne Australia Departments of Medicine/Oncology Chemical Engineering and Material Sciences University of Southern California CA United States Department of Pathology and Laboratory Medicine Weill-Cornell Medicine New YorkNY United States Department of Applied Mathematics University of CaliforniaMerced MercedCA United States Helmholtz Center Munich and Department of Mathematics Institute of Computational Biology Technical University of Munich Germany Charles Perkins Centre and School of Mathematics and Statistics University of Sydney Australia Departments of Oncology Convergence Institute Biomedical Engineering and Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD United States

Biomedical research centers can empower basic discovery and novel therapeutic strategies by leveraging their large-scale datasets from experiments and patients. This data, together with new technologies to create and analyze it, has ushered in an era of data-driven discovery which requires moving beyond the traditional individual, single-discipline investigator research model. This interdisciplinary niche is where computational biology thrives. It has matured over the past three decades and made major contributions to scientific knowledge and human health, yet researchers in the field often languish in career advancement, publication, and grant review. We propose solutions for individual scientists, institutions, journal publishers, funding agencies, and educators. © 2021, CC BY-SA.

关键词： Large dataset