  Despite the exponential overhead to describe general multi-qubit quantum
states and processes, efficient methods for certain state families and
operations have been developed and utilised. The stabilizer formalism and the
Gottesman-Knill theorem, where pure stabilizer or graph states are manipulated
by Clifford operations and Pauli measurements, are prominent examples, and
these states play a major role in many applications in quantum technologies.
Here we develop a noisy stabilizer formalism, i.e., a method that allows one
not only to efficiently describe and follow pure states under Clifford
operations and Pauli measurements but also Pauli noise processes acting on such
stabilizer states, including uncorrelated and correlated dephasing and single-
or multi-qubit depolarizing noise. The method scales linearly in the number of
qubits of the initial state, but exponentially in the size of the target state.
Thus, whenever a noisy stabilizer state is manipulated by means of local Pauli
measurements such that a multipartite entangled state of a few qubits is
generated, one can efficiently describe the resulting state.
