  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.
