Random Quantum Hamiltonians: Physics, Computation, and Complexity

Disordered models are the canonical starting point for probing emergent behaviour in complex systems. First motivated by magnetism in materials, the theory of disordered systems now spans physics, mathematics, computer science, statistics and machine learning. Random quantum Hamiltonians, the quantum variants of these models, show phenomena such as quantum chaos, entanglement growth and holographic dualities that remain poorly understood. This IPAM workshop convenes mathematicians, physicists and computer scientists to map the state of the art, formulate open problems and chart new directions. Core themes are rigorous understanding of spectral properties, analysis of thermalisation and bridges to holography, linked to computational questions including the average-case hardness of simulating these systems with quantum or classical computers and the formulation of classically hard problems suited to quantum computers. The programme includes a poster session; registration includes a remote-participation option.