Fast Algorithms for Quantum Signal Processing - IPAM at UCLA

Explore fast algorithms for quantum signal processing in this 35-minute conference talk presented by Yulong Dong at IPAM's Quantum Numerical Linear Algebra Workshop. Delve into the unified viewpoint of quantum algorithms provided by quantum singular value transformation (QSVT) and the quantum signal processing (QSP) method of polynomial representation. Learn about optimization-based fast algorithms for solving large-scale QSP problems, recent progress in understanding the energy landscape of optimization problems, and the duality between target function smoothness and phase factor decay rates. Discover insights into solving linear systems, Hamiltonian simulation, and the importance of symmetric phase factors in optimization landscapes. Gain knowledge about the Quantum Signal Processing PACKage (OSPPACK) and techniques for streamlining the process of finding phase factors using matrix product state structures and gradient calculations.

Intro
Goal of OSP (real case)
Algorithms for finding phase factors
Optimization based formulation
Symmetric OSP
Example: Solve linear systems
Example: Hamiltonian simulation
Quantum Signal Processing PACKage OSPPACKO Source Code
Streamlining the process of finding phase factors
Symmetric phase factors are important to the landscape
Optimization landscape
Uniqueness of symmetric phase factor
Key: Lauren polynomials
Distance of maximal solution to
Matrix product state structure of GSP
Gradient calculation