: Previous work has shown that Gibbs state preparation is a key primitive for semidefinite programming (SDP) algorithms, and that classical Gibbs distributions play an analogous role for linear programs (LP), both within the multiplicative-weights framework. This talk extends that perspective to other symmetric cones, focusing on second-order cone programs (SOCPs), and identifies additional quantum states that serve as optimization primitives for these problem classes. I will present quantum methods to approximately solve SOCPs within a multiplicative-weights framework, using QRAM and block-encoding techniques, and compare them to their appropriate classical counterparts. With this approach, our quantum algorithms achieve runtimes close to those known for linear programming. As an application of the framework, we consider portfolio optimization via SDP relaxations and examine the challenges and advantages of using these Gibbs states based optimization routines.
Copyright. All Rights Reserved.