Abstract
In this talk, I will present a quantum algorithm known as quantum singular value transformation (QSVT), which applies polynomial transformations to the singular values of high-dimensional matrices. In Part 1, I will cover the mathematical preliminaries underlying the algorithm, including matrix decompositions (singular value decomposition and cosine-sine decomposition), the nonlinear Fourier transform, and selected results on uniform polynomial approximation. In Part 2, I will introduce the main components of the algorithm, including block encoding and quantum signal processing. As an application, I will describe a quantum linear system solver with optimal scaling in the condition number based on the block preconditioning technique, and discuss strategies to go beyond the condition number barrier.
Yuan Su
Senior Applied Scientist
I work on quantum algorithms for simulating Hamiltonian dynamics. I am particularly interested in the design, analysis, implementation, and application of quantum simulation.