Complexity of Learning and Creating Quantum Systems

The complexity of a quantum system is a concept of fundamental interest in quantum information, quantum computing, and, more recently, in the study of quantum black holes. In this talk, I will present three notions of complexity for learning and creating quantum systems, including (1) the minimum gates needed to create the state, (2) the minimum number of measurements needed to learn the state, and (3) the minimum computational time needed to learn the state. I will prove how these conceptually different notions closely relate to each other using techniques from random scrambling, learning theory, and cryptography.