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

Recent progress in quantum computing shows the need to incorporate many branches of mathematics (graph theory, matrix theory, optimization, theory of orthogonal polynomials and more) into physics, computer science and chemistry. At the 2024 SIAM Quantum Intersections Convening, Bert de Jong (Lawrence Berkeley National Laboratory) gave a talk entitled 'Quantum Science Needs Mathematicians' (Report of the SIAM Quantum Intersections Convening. Integrating Mathematical Scientists into Quantum Research, 7-9 October 2024, Tysons, Virginia (doi:10.11337/25M1741017)), since despite the growing demand for research in these domains, the mathematical sciences community has remained largely disengaged from quantum research, with only a few isolated areas of active involvement. This issue brings together researchers from different areas of mathematics to show the relation between spectral graph theory, the theory of orthogonal polynomials and numerical analysis. This interconnectedness highlights the versatility and importance of these areas of mathematics in the context of quantum computing.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.