We introduce a novel approach to evaluate the nonstabilizerness of an $N$-qubits matrix product state (MPS) with bond dimension $\chi$. In particular, we consider the recently introduced stabilizer Rényi entropies (SREs). We show that the exponentially hard evaluation of the SREs can be achieved by means of a simple perfect sampling of the many-body wave function over the Pauli string configurations. The sampling is achieved with a novel MPS technique, which enables us to compute each sample in an efficient way with a computational cost $O(N{\chi }^3)$. We benchmark our method over randomly generated magic states, as well as in the ground-state of the quantum Ising chain. Exploiting the extremely favorable scaling, we easily have access to the nonequilibrium dynamics of the SREs after a quantum quench.

• Received 27 April 2023
• Accepted 5 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.180401