We present two Diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a discrete spin generalization of the T- moves spin-orbit DMC, which provides an upper bound to the fixed-phase energy. The second is a spin-integrated DMC method which recovers the fixed-phase property by avoiding the definition of the effective Hamiltonian involved in the T-moves approach. The latter is a more accurate method but it is restricted to spin-independent two-body interactions. We report a comparison between both algorithms for different systems. As a check of the efficiency of both methods, we compare the DMC energies with results obtained with other numerical methods, finding agreement between both estimation
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