Quantum Computing and Scientific Computing

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 1449

Special Issue Editor

Department of Industrial and Systems Engineering, Lehigh University, 27 Memorial Dr W, Bethlehem, PA 18015, USA
Interests: uncertainty quantification; physics-informed machine learning; quantum computing;scientific computing

Special Issue Information

Dear Colleagues,

The recent development of quantum algorithms has significantly pushed forward the frontier of using quantum computers for solving a wide range of scientific computing problems even in the NISQ era. This Special Issue aims at publishing original scientific articles devoted to advances in quantum computing algorithms for scientific computing. These advances include solving numerical linear algebra tasks, e.g, solving linear systems, eigenvalue decomposition, singular value decomposition; solving large-scale continuous/discrete optimization problems; and solving certain high dimensional linear and nonlinear differential equations. This Special Issue of/Mathematics/welcomes academic and industrial research on quantum computing.

Dr. Xiu Yang
Guest Editor

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Keywords

  • quantum algorithms for numerical linear algebra
  • quantum algorithms for optimization
  • quantum algorithms for solving ordinary/partial/fractional differential equations
  • quantum algorithms for scientific machine learning
  • quantum algorithms for simulating complex systems in scientific or engineering problems
  • uncertainty quantification in quantum scientific computing algorithms
  • quantum simulators for quantum scientific computing

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Published Papers (1 paper)

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Research

16 pages, 895 KiB  
Article
Koopman Spectral Linearization vs. Carleman Linearization: A Computational Comparison Study
by Dongwei Shi and Xiu Yang
Mathematics 2024, 12(14), 2156; https://doi.org/10.3390/math12142156 - 9 Jul 2024
Viewed by 849
Abstract
Nonlinearity presents a significant challenge in developing quantum algorithms involving differential equations, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. Instead, this paper introduces the Koopman Spectral Linearization method tailored for nonlinear autonomous ordinary differential equations. This innovative linearization [...] Read more.
Nonlinearity presents a significant challenge in developing quantum algorithms involving differential equations, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. Instead, this paper introduces the Koopman Spectral Linearization method tailored for nonlinear autonomous ordinary differential equations. This innovative linearization approach harnesses the interpolation methods and the Koopman Operator Theory to yield a lifted linear system. It promises to serve as an alternative approach that can be employed in scenarios where Carleman Linearization is traditionally applied. Numerical experiments demonstrate the effectiveness of this linearization approach for several commonly used nonlinear ordinary differential equations. Full article
(This article belongs to the Special Issue Quantum Computing and Scientific Computing)
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