Quantum Magic via Perfect Pauli Sampling of Matrix Product States

• URL: http://arxiv.org/abs/2303.05536v2
• Date: Wed, 19 Apr 2023 10:43:28 GMT
• Title: Quantum Magic via Perfect Pauli Sampling of Matrix Product States
• Authors: Guglielmo Lami, Mario Collura
• Abstract summary: We consider the recently introduced Stabilizer R'enyi 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a novel breakthrough 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 R\'enyi 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 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 favourable scaling, we easily have access to the non-equilibrium dynamics of the SREs after a quantum quench.

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