QMA vs. QCMA and Pseudorandomness in Quantum Complexity Theory

Explore a computer science seminar that delves into the fascinating realm of quantum complexity theory, specifically examining the relationship between QMA and QCMA - two different generalizations of NP. Learn about the fundamental differences between these complexity classes, where QMA allows quantum state witnesses while QCMA requires classical string witnesses. Discover the ongoing investigation into whether a separation exists between these classes and understand how this connects to quantum pseudorandomness. Examine a new theoretical framework that establishes a "win-win" scenario: either proving a classical oracle separation between QMA and QCMA, or demonstrating quantum advantage in distinguishing pseudorandom distributions on permutations. Investigate the connection between this research and the Aaronson-Ambainis conjecture, all presented in an accessible manner requiring no prior knowledge of quantum computation. The presentation includes collaborative research findings from Henry Yuen, Jiahui Liu, and Saachi Mutreja, offering insights into cutting-edge developments in quantum complexity theory.