Analytical and Compressed Simulation of Noisy Stabilizer Circuits

We develop analytical and algorithmic techniques that enable efficient simulation of a broad class of noisy stabilizer circuits. We derive closed-form expressions of expectation values for tensor product of Paulis in circuits with non-deterministic Pauli measurements, yielding an efficient strong simulation method that avoids explicit density matrix construction and enables direct noise parameter sweeps. We introduce a circuit compression framework that reduces the per-sample cost of weak simulation in general noisy stabilizer circuits, including deterministic measurements, by separating parameter-independent preprocessing from sampling. Finally, we extend the analytical framework beyond its standard domain to include a small number of deterministic measurements, general rotations, and non-diagonal noise channels. Our results provide a unified framework for both strong and weak simulation of noisy stabilizer circuits and corresponds to an extension of the noisy stabilizer formalism introduced in \cite{PhysRevA.107.032424}. They offer applications ranging from calculation of the expectation values of entanglement witnesses, determination of reduced states, to energy evaluation.