Learning the stabilizer group of a Matrix Product State

• URL: http://arxiv.org/abs/2401.16481v1
• Date: Mon, 29 Jan 2024 19:00:13 GMT
• Title: Learning the stabilizer group of a Matrix Product State
• Authors: Guglielmo Lami, Mario Collura
• Abstract summary: We present a novel classical algorithm designed to learn the stabilizer group of a given Matrix Product State (MPS) We benchmark our method on $T$-doped states randomly scrambled via Clifford unitary dynamics. Our method, thanks to a very favourable scaling $mathcalO(chi3)$, represents the first effective approach to obtain a genuine magic monotone for MPS.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel classical algorithm designed to learn the stabilizer group -- namely the group of Pauli strings for which a state is a $\pm 1$ eigenvector -- of a given Matrix Product State (MPS). The algorithm is based on a clever and theoretically grounded biased sampling in the Pauli (or Bell) basis. Its output is a set of independent stabilizer generators whose total number is directly associated with the stabilizer nullity, notably a well-established nonstabilizer monotone. We benchmark our method on $T$-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly-entangled MPS with bond dimension $\chi\sim 10^3$. Our method, thanks to a very favourable scaling $\mathcal{O}(\chi^3)$, represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out-of-equilibrium.

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