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Holographic software for quantum networks

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Science China Mathematics 2018年第4期61卷 593-626页

作者： Arthur Jaffe Zhengwei Liu Alex Wozniakowski Departments of Mathematics and Physics Harvard UniversityCambridgeMA 02138USA School of physical and mathematical sciences and Complexity Institute Nanyang Technological UniversitySingapore 637723Singapore

We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform(SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the n-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.

关键词： quantum information picture language string Fourier transform Clifford gate multipartite entanglement quantum protocol

Topological feature engineering for machine learning based halide perovskite materials design

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npj Computational Materials 2022年第1期8卷 1943-1950页

作者： D.Vijay Anand Qiang Xu JunJie Wee Kelin Xia Tze Chien Sum Division of mathematical sciences School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore637371Singapore Division of Physics&Applied Physics School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore637371Singapore

Accelerated materials development with machine learning(ML)assisted screening and high throughput experimentation for new photovoltaic materials holds the key to addressing our grand energy ***-driven ML is envisaged as a decisive enabler for new perovskite materials ***,its full potential can be severely curtailed by poorly represented molecular descriptors(or fingerprints).Optimal descriptors are essential for establishing effective mathematical representations of quantitative structure-property *** we reveal that our persistent functions(PFs)based learning models offer significant accuracy advantages over traditional descriptor based models in organic-inorganic halide perovskite(OIHP)materials design and have similar performance as deep learning *** multiscale simplicial complex approach not only provides a more precise representation for OIHP structures and underlying interactions,but also has better transferability to ML *** results demonstrate that advanced geometrical and topological invariants are highly efficient feature engineering approaches that can markedly improve the performance of learning models for molecular data ***,new structure-property relationships can be established between our invariants and *** anticipate that our molecular representations and featurization models will transcend the limitations of conventional approaches and lead to breakthroughs in perovskite materials design and discovery.

关键词： perovskite halide invariants

A classical algorithm to mimic quantum decisions

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National Science Review 2019年第4期6卷 608-609页

作者： Mile Gu School of physical and mathematical sciences Nanyang Technological University

In his famous 1982 lecture, Nobel laureate Richard Feynman seeded the idea of quantum computation. He reasoned that the amount of classical information required to describe a quantum system scaled exponentially with its size, and thus could not be efficiently simulated by a classical computer. Indeed, a fairly modest system of 100 quantum bits would already require more information to describe than all the present data storage

关键词： A classical algorithm to mimic quantum decisions

Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems Science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong School of physical and mathematical sciences Nanjing Tech UniversityNanjing 211816China School of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

Langrangian formulation and solitary wave solutions of a generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

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Journal of Ocean Engineering and Science 2023年第2期8卷 152-168页

作者： Chaudry Masood Khalique Oke Davies Adeyemo International Institute for Symmetry Analysis and mathematical Modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear *** obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration ***,we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular ***,we secure,singular and nonsingular(periodic)soliton solutions,cnoidal,snoidal as well as dnoidal wave ***,we depict the dynamics of the solutions using suitable *** application of obtained results in various fields of sciences and engineering are *** conclusion,we construct conserved currents of the aforementioned equation via Noether’s theorem(with Helmholtz criteria)and standard multiplier technique through the homotopy formula.

关键词： Generalized Zakharov-Kuznetsov equation with dual power-law nonlinearity Lie point symmetries Exact solutions Cnoidal and snoidal wave solutions Conserved currents

High-Efficiency Wide-Band Cross-Polarization Conversion Using Bi-layered Metal Hole Pairs

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Chinese Physics Letters 2018年第10期35卷 40-43页

作者： Yong Zhang Xian-Ke Li Cheng-Ping Huang Department of Physics School of Physical and Mathematical Sciences Nanjing Tech University

We present a polarization converter composed of bi-layered metal films perforated with rectangle hole pairs in each film. The proposed converter can convert the polarization of an incident linearly-polarized electromagnetic wave to its orthogonal direction with high efficiency and large bandwidth in the infrared or microwave *** make sure of the mechanism of polarization conversion, the current and electric-field distributions at different resonant frequencies are analyzed. It is found that the cross-polarized transmission is due to the near-field coupling between hole pairs in neighboring metal films. Finally, a prototype of the proposed converter is fabricated and measured in the microwave region. Good agreement between the experimental and simulated results is obtained.

关键词： High-Efficiency Wide-Band Cross-Polarization Conversion Using Bi-layered Metal Hole Pairs

Efficient Dual Algorithms for Image Segmentation Using TV-Allen-Cahn Type Models

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Communications in Computational Physics 2011年第4期9卷 859-877页

作者： Li-Lian Wang Ying Gu Division of mathematical sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

Variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn *** commonlyused numerical approaches usually suffer from the difficulties not only with the nondifferentiability of the TV-term,but also with directly evolving the discontinuous piecewise constant-structured *** this paper,we propose efficient dual algorithms to overcome these *** use of a splitting-penalty method results in TVAllen-Cahn type models associated with different"double-well"potentials,which allow for the implementation of the dual algorithm of Chambolle[8].Moreover,we present a new dual algorithm based on an edge-featured penalty of the dual variable,which only requires to solve a vectorial Allen-Cahn type equation with linear∇(div)-diffusion rather than fully nonlinear diffusion in the Chambolle’s ***,more efficient numerical algorithms such as time-splitting method and Fast Fourier Transform(FFT)can be *** numerical tests show that two dual algorithms are much faster and more stable than the primal gradient descent approach,and the new dual algorithm is at least as efficient as the Chambolle’s algorithm but is more *** demonstrate that the new method also provides a viable alternative for image restoration.

关键词： Variational models image segmentation TV-Allen-Cahn type equations dual algorithms splitting-penalty methods FFT.

On Spectral Approximations by Generalized Slepian Functions

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Numerical Mathematics(Theory,Methods and Applications) 2011年第2期4卷 296-318页

作者： Jing Zhang Li-Lian Wang Division of mathematical sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

We introduce a family of orthogonal functions,termed as generalized Slepian functions(GSFs),closely related to the time-frequency concentration problem on a unit disk in ***[19].These functions form a complete orthogonal system in L_(ωα)^(2)(−1,1)with̟ω_(α)(x)=(1−x)^(α),α>−1,and can be viewed as a generalization of the Jacobi polynomials with parameter(α,0).We present various analytic and asymptotic properties of GSFs,and study spectral approximations by such functions.

关键词： Generalized Slepian functions orthogonal systems approximation errors spectral accuracy

Topological entropy of sets of generic points for actions of amenable groups

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Science China Mathematics 2018年第5期61卷 869-880页

作者： Dongmei Zheng Ercai Chen School of physical and mathematical sciences Nanjing Tech University School of mathematical sciences and Institute of Mathematics Nanjing Normal University

Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).

关键词： entropy generic point amenable group variational principle