We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends on the number of magic states used in the quantum computation, and not on the length of the gate and measurement sequence.
@article{arxiv.2004.01992,
title = {A hidden variable model for universal quantum computation with magic states on qubits},
author = {Michael Zurel and Cihan Okay and Robert Raussendorf},
journal= {arXiv preprint arXiv:2004.01992},
year = {2021}
}