Learning the stabilizer group of a Matrix Product State
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911767381147648 |
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| author | Lami, Guglielmo Collura, Mario |
| author_facet | Lami, Guglielmo Collura, Mario |
| contents | 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 $χ\sim 10^3$. Our method, thanks to a very favourable scaling $\mathcal{O}(χ^3)$, represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out-of-equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning the stabilizer group of a Matrix Product State Lami, Guglielmo Collura, Mario Quantum Physics 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 $χ\sim 10^3$. Our method, thanks to a very favourable scaling $\mathcal{O}(χ^3)$, represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out-of-equilibrium. |
| title | Learning the stabilizer group of a Matrix Product State |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.16481 |