Quantum State Learning Implies Circuit Lower Bounds

Watch a conference talk from TQC 2024 exploring the deep connections between quantum state learning and circuit complexity theory. Delve into groundbreaking research that establishes relationships between state tomography, pseudorandomness, state synthesis lower bounds, and classical circuit lower bounds. Learn how the existence of efficient algorithms for distinguishing quantum states implies important complexity theoretic consequences, including potential breakthroughs in classical circuit complexity. Explore parallel results between quantum learning of Boolean functions and circuit lower bounds, along with the construction of conditional pseudorandom states secure against uniform sub-exponential-time quantum computations. Discover new circuit size hierarchy theorems for non-uniform state synthesis and their connections to complexity class separations. This presentation from the 19th Conference on the Theory of Quantum Computation, Communication and Cryptography offers valuable insights for researchers and students working in theoretical quantum information science and computational complexity theory.