Analytical and Compressed Simulation of Noisy Stabilizer Circuits

TL;DR

This paper introduces analytical and algorithmic techniques for efficient simulation of noisy stabilizer circuits, enabling both strong and weak simulation with reduced computational costs and extended noise models.

Contribution

It develops a unified framework for simulating noisy stabilizer circuits, including new closed-form expressions and a circuit compression method for improved efficiency.

Findings

Derived closed-form expectation values for tensor products of Paulis.

Introduced a circuit compression framework reducing per-sample cost.

Extended the analytical framework to include deterministic measurements and non-diagonal noise channels.

Abstract

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.