  We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D
phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009
(2023)]. By introducing an additional $SU(2)$ layer degree of freedom, we
reformulate the model into a form suitable for sign-problem-free QMC
simulation. From the finite-size-scaling, we show that this QMC-friendly model
undergoes a quantum phase transition belonging to the 3D Ising universality
class, and at the critical point we compute the scaling dimensions from the
state-operator correspondence, which largely agrees with the prediction from
the conformal field theory. These results pave the way to construct
sign-problem-free models for QMC simulations on the fuzzy sphere, which could
advance the future study on more sophisticated criticalities.
