Quantum Fourier Transform Beyond Shor's Algorithm - Part 3

Explore advanced applications of Quantum Fourier Transform (QFT) in this 59-minute lecture from the 2023 PCMI Graduate Summer School on Quantum Computation. Delve into modern QFT applications beyond the hidden subgroup problem, including Jordan's gradient computation algorithm and its applications in convex optimization, distribution learning, and quantum tomography. Learn about recent improvements to phase estimation, including bias removal and coherent boosting techniques. Examine QFT from the Heisenberg picture perspective, understanding operator Fourier transform and its quantum computing implications. Access comprehensive lecture notes and two problem sets to reinforce understanding of these advanced quantum computing concepts. Part of a broader three-week summer program featuring expert-led minicourses on quantum computing, this lecture combines theoretical depth with practical problem-solving sessions.