  Quantum error correcting codes typically do not account for quantum state
transitions - leakage - out of the computational subspace. Since these errors
can last for multiple detection rounds they can significantly contribute to
logical errors. It is therefore important to understand how to numerically
model them efficiently. Fully quantum simulations of leakage require more
levels per leaked qubit, which substantially limits the system sizes that may
be simulated. To address this, we introduce a Random Phase Approximation (RPA)
on quantum channels that preserves the incoherence between the computational
and leakage subspaces. The assumption of incoherence enables the quantum
simulation of leakage at little computational overhead. We motivate the
approximation's validity by showing that incoherence is achieved naturally
during repeated stabilizer measurements. Additionally, we provide various
simulation results which show that the RPA yields accurate error correction
statistics in the repetition and surface codes with physical error parameters.
