Optimization Algorithms Using Gibbs State Preparation and Beyond

Watch this 49-minute conference talk exploring advanced quantum optimization algorithms that extend beyond traditional Gibbs state preparation methods. Discover how Gibbs state preparation serves as a fundamental primitive for semidefinite programming (SDP) algorithms and learn about the analogous role classical Gibbs distributions play in linear programming within the multiplicative-weights framework. Explore the extension of this perspective to other symmetric cones, particularly focusing on second-order cone programs (SOCPs), and examine additional quantum states that function as optimization primitives for these problem classes. Gain insights into quantum methods for approximately solving SOCPs using QRAM and block-encoding techniques within a multiplicative-weights framework, and understand how these approaches compare to their classical counterparts. Learn how quantum algorithms achieve runtimes comparable to those known for linear programming and see practical applications through portfolio optimization via SDP relaxations. Examine the challenges and advantages of implementing Gibbs states-based optimization routines in real-world scenarios, presented by M. Isabel Franco Garrido from the California Institute of Technology at IPAM's New Frontiers in Quantum Algorithms for Open Quantum Systems Workshop.