Quantum Computing Meets Numerical Linear Algebra

 In this talk, we explore the intersection of quantum computing and numerical linear algebra by examining the quantum Fourier transform (QFT). The QFT is used as a part of many of the most successful quantum algorithms proposed to date, including Shor’s integer factoring algorithm. We derive the QFT from a matrix analysis perspective that requires only basic knowledge of linear algebra. This alternative approach uses standard matrix operations to decompose the discrete Fourier transform matrix, revealing its underlying Kronecker product structure, which can be interpreted as the quantum Fourier transform. This interpretation provides a straightforward pathway to constructing the corresponding quantum circuit. We also introduce qclab++, a high-performance, fully-templated C++ library designed for GPU-accelerated quantum circuit simulations, featuring highly optimized algorithms for various quantum gates and leveraging OpenMP offloading for portability and performance. Additionally, we present qclab, a quantum circuit toolbox for Matlab that mirrors the syntax of qclab++, offering the flexibility of a scripting language with high-performance GPU acceleration when needed. Benchmark comparisons, including simulations on NERSC’s Perlmutter system, demonstrate qclab++'s substantial speedups and competitiveness with other quantum circuit simulation packages.

Bio
Roel Van Beeumen is a Staff Scientist in the Applied Mathematics and Computational Research Division at Berkeley Lab. His research interests range from numerical linear algebra and software for solving large-scale and high dimensional eigenvalue problems to quantum computing and quantum algorithms. He earned his PhD in Engineering Science: Computer Science (2015) at KU Leuven in Belgium, from which he also holds Master degrees in Mathematical Engineering (2010) and in Archaeology (2011).
http://www.roelvanbeeumen.be/