Title: Vector Ising Spin Annealer for Minimizing Ising Hamiltonians

Abstract: We introduce the Vector Ising Spin Annealer (VISA), a framework in gain-based computing that harnesses light-matter interactions to solve complex optimization problems encoded in spin Hamiltonians. Traditional driven-dissipative systems often select excited states due to limitations in spin movement. VISA transcends these constraints by enabling spins to operate in a three-dimensional space, offering a robust solution to minimize Ising Hamiltonians effectively. Our comparative analysis reveals VISA's superior performance over conventional single-dimension spin optimizers, demonstrating its ability to bridge substantial energy barriers in complex landscapes. Through detailed studies on cyclic and random graphs, we show VISA's proficiency in dynamically evolving the energy landscape with time-dependent gain and penalty annealing, illustrating its potential to redefine optimization in physical systems.