Description
Boson sampling provides a promising route toward demonstrating quantum computational advantage, but its experimental implementation remains challenging due to demanding physical resource requirements. In this talk, I will discuss two approaches to extending boson sampling beyond idealized bosonic systems. First, I will introduce a higher-spin sampling framework in which finite-dimensional spin systems approximate Fock-state boson sampling. We establish a quasi-linear mode scaling relation, (m\sim n^{1+3/(2S)}), showing how increasing the spin quantum number reduces the required resources while preserving the relevant sampling complexity. Second, I will discuss computational complexity in open bosonic systems, focusing on the fixed points of Lindblad dynamics. Different dissipative mechanisms can produce classically tractable steady states or stabilize nonclassical states with potentially challenging sampling tasks. Together, these directions provide a framework for understanding how quantum computational complexity survives finite-dimensional approximations and environmental interactions.