Quantum Algorithms from Polynomials: Solving Linear Systems Faster - Lecture

Explore quantum algorithms derived from polynomials in this comprehensive lecture on solving linear systems faster. Gain insights into recent techniques like linear combinations of unitaries (LCU) and the quantum singular value transformation framework (QSVT). Discover how these approaches reduce quantum algorithmic problems to finding optimal polynomial approximations for specific functions, with a focus on the inverse function. Learn about the application of these techniques to solve linear systems of equations, including improvements on prior work that achieve constant factor enhancements. Delve into the research presented in https://arxiv.org/abs/2109.04248, a collaborative effort with Daniel Szilagyi and Iordanis Kerenidis. This Team-Net QC Colloquium 2022 presentation covers cutting-edge topics in quantum computing, including near-term quantum algorithms, quantum supremacy experiments, and practical quantum error correction.