Article
Physics, Mathematical
Kaifeng Bu, Dax Enshan Koh
Summary: This article offers an efficient algorithm to evaluate a certain class of exponential sums and explores their applications in classical simulation of quantum circuits and the Holant framework.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Optics
Michael Streif, Sheir Yarkoni, Andrea Skolik, Florian Neukart, Martin Leib
Summary: In this study, we utilized quantum approximate optimization algorithm to solve the APX-hard optimization problem in the automotive industry known as the binary paint shop problem (BPSP). Our results demonstrate that QAOA with constant depth outperforms all known heuristics for the BPSP in the infinite size limit. The study was concluded with successful experiments on small instances using a trapped-ion quantum computer via Amazon Braket.
Article
Physics, Multidisciplinary
Sergey Bravyi, David Gosset, Yinchen Liu
Summary: This paper describes and analyzes algorithms for classically simulating measurements of n-qubit quantum states in the standard basis. The algorithms reduce the sampling task and accelerate quantum circuit simulations and measurement-based quantum computation with the surface code resource state.
PHYSICAL REVIEW LETTERS
(2022)
Article
Computer Science, Information Systems
Amina Benkessirat, Nadjia Benblidia
Summary: In real-life classification applications, it can be challenging to select model features that adequately classify samples from a large number of candidates. This article's main contributions include evaluating the relevance and redundancy of features, defining the feature selection problem as an eigenvalue computation problem with a linear constraint, and efficiently selecting the best features. The approach was tested on 20 UCI benchmark datasets and compared with other widely used and state-of-the-art approaches. The experimental results showed that our approach improved the classification task by using only 20% of the conventional features.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2022)
Article
Mathematics, Applied
Fei Xu, Manting Xie, Qiumei Huang, Meiling Yue, Hongkun Ma
Summary: A new type of adaptive multigrid method is proposed for solving multiple eigenvalue problems, achieving the same efficiency as the adaptive multigrid method by solving linear boundary value problems and eigenvalue problems in a low-dimensional space.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Lingling Sun, Yidu Yang
Summary: This paper discusses the a posteriori error estimates and adaptive algorithm of non-conforming mixed finite elements for the Stokes eigenvalue problem. The reliability and efficiency of the error estimators are proven. Two adaptive algorithms, direct AFEM and shifted-inverse AFEM, are built based on the error estimators. Numerical experiments and theoretical analysis show that the numerical eigenvalues obtained by these algorithms achieve optimal convergence order and approximate the exact solutions from below.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Fei Xu, Qiumei Huang, Shuangshuang Chen, Hongkun Ma
Summary: This paper proposes an adaptive multigrid method for solving eigenvalue problems, based on the multilevel correction method and adaptive multigrid method. The method only requires solving a linear boundary value problem on each adaptive space and correcting the approximate solution by solving a low dimensional eigenvalue problem, reducing computational work significantly.
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2022)
Article
Mathematics, Applied
Stefano Giani, Luka Grubisic, Harri Hakula, Jeffrey S. Ovall
Summary: The study introduces an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems, which is effective in estimating the approximation error in eigenvalue clusters and their corresponding invariant subspaces.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Feng Du, Jing Mao, Qiaoling Wang, Changyu Xia, Yan Zhao
Summary: We prove Li-Yau-Kroger-type bounds for Neumann-type eigenvalues of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which directly implies two sharp Reilly-type inequalities for the corresponding first nonzero eigenvalue.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Multidisciplinary Sciences
Furkan Oz, Omer San, Kursat Kara
Summary: Differential equations are fundamental for modeling the physics of the universe. Solving partial and ordinary differential equations is crucial for simulating and calculating complex physical processes. Quantum computation, specifically the quantum partial differential equation (PDE) solver using the quantum amplitude estimation algorithm (QAEA), provides a promising method for solving these equations efficiently.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics
Qingchun Ji, Li Lin
Summary: Under various elliptic boundary conditions, lower eigenvalue estimates for Dirac operators are obtained using the weighted L-2-technique derived from the Morrey-Kohn-Hormander theory in several complex variables. Lower bounds in terms of the volume of the underlying manifolds are deduced from the sharp Sobolev inequality.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Quantum Science & Technology
Hakop Pashayan, Oliver Reardon-Smith, Kamil Korzekwa, Stephen D. Bartlett
Summary: Researchers present two classical algorithms for simulating universal quantum circuits, with each algorithm performing best in different parameter regimes. The ESTIMATE algorithm provides an estimate of measurement outcome probabilities with a specific precision, while the COMPUTE algorithm calculates probabilities to machine precision.
Article
Optics
Daniel Nagaj, Dominik Hangleiter, Jens Eisert, Martin Schwarz
Summary: Pinning a single qubit in a particular state can lead to difficult static questions about the ground-state properties of local Hamiltonian problems and universal quantum computation with commuting Hamiltonians. Additionally, variants of the ground-state connectivity problem in the context of pinning may exhibit quantum-classical Merlin-Arthur completeness.
Article
Optics
Changhun Oh, Kyungjoo Noh, Bill Fefferman, Liang Jiang
Summary: Characterizing the computational power of NISQ devices, particularly in the context of boson sampling, is a crucial task. This study focuses on the hardness of lossy boson sampling using MPO simulation, revealing how the computational cost of the MPO algorithm changes with input photon number. The results demonstrate an exponential scaling of time complexity for MPO simulation when the output photon number grows faster than the square root of the input photon number.
Article
Biochemical Research Methods
Arnab Mallik, Lucian Ilie
Summary: Sequence similarity is crucial in biological research, and the sensitivity of spaced seeds is essential for improving programs like BLAST. The new algorithm ALeS has been shown to produce more sensitive seeds than current programs, with accurate sensitivity estimation for arbitrary seeds.
Article
Engineering, Civil
Tino Wollmann, Marlon Hahn, Sebastian Wiedemann, Andreas Zeiser, Joern Jaschinski, Niels Modler, Nooman Ben Khalifa, Frank Meissen, Christian Paul
ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING
(2018)
Article
Mathematics, Applied
Thorsten Rohwedder, Reinhold Schneider, Andreas Zeiser
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2011)
Article
Mathematics
Andreas Zeiser
CONSTRUCTIVE APPROXIMATION
(2012)
Article
Mathematics, Applied
Andreas Zeiser
JOURNAL OF SCIENTIFIC COMPUTING
(2011)
Review
Energy & Fuels
Christof Schultz, Markus Fenske, Janardan Dagar, Andreas Zeiser, Andreas Bartelt, Rutger Schlatmann, Eva Unger, Bert Stegemann
Proceedings Paper
Materials Science, Multidisciplinary
Christof Schultz, Markus Fenske, Janardan Dagar, Guillermo A. Farias Basulto, Andreas Zeiser, Andreas Bartelt, Cornelia Junghans, Rutger Schlatmann, Eva Unger, Bert Stegemann
Summary: This study investigates the use of nanosecond and picosecond laser pulses for patterning CIGSe and metal halide perovskite solar cell absorber layers. The results show that the laser pulses lead to material modification in the vicinity of the scribed lines for CIGSe, but not for perovskite absorber layers. Numerical calculations suggest that this effect is due to the lower thickness of the perovskite layer and the higher laser fluence required for perovskite ablation. The unaffected edge regions in perovskite enable a reduction of the dead area width and an increase in power conversion efficiency and fill factor.
MATERIALS TODAY-PROCEEDINGS
(2022)
Article
Materials Science, Multidisciplinary
A Zeiser, N Bücking, J Förstner, A Knorr
Article
Physics, Multidisciplinary
L Töben, L Gundlach, R Ernstorfer, R Eichberger, T Hannappel, F Willig, A Zeiser, J Förstner, A Knorr, PH Hahn, WG Schmidt
PHYSICAL REVIEW LETTERS
(2005)
Article
Physics, Condensed Matter
A Zeiser, N Bücking, J Götte, J Förstner, P Hahn, WG Schmidt, A Knorr
PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS
(2004)
