Quantum Hamiltonian Complexity - Lecture 1

Explore quantum systems and computational complexity in this lecture from the Park City Mathematics Institute's Graduate Summer School series, delivered by Sandy Irani from UC Irvine. Dive into the fundamental challenges of computing properties of quantum systems and simulating their behavior over time. Learn about formal complexity-theoretic approaches to understanding quantum systems, with particular focus on determining ground states and their computational requirements in both finite and infinite systems. Examine key concepts including Hermitian operators, local Hamiltonians, spin liquids, and weighted constraint satisfaction problems. Investigate the relationships between classical and quantum computational complexity through topics like Boolean satisfiability, NP problems, quantum verifiers, and the Local Hamiltonian problem. Part of a comprehensive three-week program on quantum computation, this lecture connects to broader themes in quantum learning, information theory, and the analysis of near-term quantum devices. Access supplementary materials including detailed lecture notes and problem sets to deepen understanding of the presented concepts.