Join a technical seminar exploring the intersection of quantum error correction and quantum metrology, featuring researcher Sisi Zhou. Discover how quantum metrology's applications span from frequency spectroscopy to gravitational wave detection, while examining the Heisenberg limit - a fundamental constraint on estimation precision in quantum systems. Learn about recent breakthroughs in achieving the Heisenberg limit in noisy quantum systems through quantum error correction protocols, including necessary and sufficient conditions for success. Explore how these protocols can be optimized using semidefinite programs and examine practical examples in typical noisy systems. Understand how even when the Heisenberg limit cannot be achieved, estimation techniques still offer significant improvements over classical approaches through approximate quantum error correction.