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Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms.

Anastasiia Minenkova1, Gamal Mograby2, Hanmeng Zhan3

  • 1University of Hartford, West Hartford, CT, USA.

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Summary
This summary is machine-generated.

Quantum computing requires diverse mathematical expertise. This research highlights the crucial links between spectral graph theory, orthogonal polynomials, and numerical analysis for advancing quantum algorithms.

Keywords:
orthogonal polynomialsquantum computingspectral graph theory

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Area of Science:

  • Mathematics
  • Computer Science
  • Quantum Computing

Background:

  • Quantum computing advancements necessitate integrating various mathematical fields like graph theory and optimization.
  • The mathematical sciences community remains largely uninvolved in quantum research despite growing demand.

Purpose of the Study:

  • To demonstrate the interconnectedness of spectral graph theory, orthogonal polynomials, and numerical analysis.
  • To highlight the importance of these mathematical areas for quantum computing applications.

Main Methods:

  • Review of research connecting spectral graph theory, orthogonal polynomials, and numerical analysis.
  • Exploration of the relevance of these mathematical disciplines to quantum algorithms.

Main Results:

  • Established clear relationships between spectral graph theory, orthogonal polynomials, and numerical analysis.
  • Demonstrated the versatility and significance of these mathematical areas in quantum computing.

Conclusions:

  • The integration of mathematical sciences is vital for the progress of quantum computing.
  • Further research into these interdisciplinary connections can accelerate quantum algorithm development.