Local Hamiltonians and Quantum Cuts: Exploring the Quantum Heisenberg Model

Explore quantum computing concepts in this 59-minute lecture where Professor Alexandra Kolla from UC Santa Cruz delves into the quantum Heisenberg model and its generalizations, particularly focusing on the Quantum Max-d-Cut problem. Learn about spin glass Hamiltonians with nearest-neighbor interactions, understanding both their significance in condensed matter physics and their connection to computer science through the Max-Cut problem. Discover the complexities of the Quantum Max-d-Cut model, which handles interactions of spins with local Hilbert space of dimension d, and understand its universal nature and QMA-hard optimization characteristics. Examine recent developments in classical approximation algorithms for Quantum Max-Cut, investigate the systematic study of Quantum Max-d-Cut, and explore preliminary algorithmic approaches for approximating the ground state of corresponding Hamiltonians.