Explore recent algorithmic primitives in quantum computation with a focus on Linear Combination of Unitaries (LCU) and Quantum Signal Processing (QSP) in this 45-minute lecture by Robin Kothari from Microsoft Research. Delve into probabilistic implementations, classical repetition, and oblivious amplitude amplification (OAA) as foundational concepts. Examine the LCU method and its application to Hamiltonian simulation, along with other practical uses. Investigate eigenvalue transformation and the process of setting up the "Signal" in quantum systems. Gain insights into the challenges and advancements in quantum computation, concluding with a comprehensive recap of these cutting-edge algorithmic techniques.