Quantum Hamiltonian Complexity - Lecture 3

Learn about quantum Hamiltonian complexity in this advanced lecture from Professor Sandy Irani at the University of California, Irvine, delivered as part of the IAS/PCMI Park City Mathematics Institute's 2023 program on Quantum Computation. Explore fundamental concepts in quantum systems from a computational complexity perspective, focusing on how to compute essential properties and simulate quantum systems over time. Delve into the challenges of determining a system's lowest energy state (ground state), examining both finite and infinite systems while analyzing the computational resources needed for these calculations. Engage with topics including quantum verifier circuits, computation states, varieties of Hamiltonians, NP-hard problems, clock states, configuration graphs, translation invariance, and oracle classes through comprehensive lecture materials and accompanying problem sessions. Part of a broader summer program featuring leading experts in quantum computation, this lecture contributes to understanding the mathematical foundations necessary for building and analyzing near-term quantum devices.