Lami Guglielmo, Collura Mario
<a href="https://ror.org/004fze387">International School for Advanced Studies (SISSA)</a>, 34136 Trieste, Italy.
Laboratoire de Physique Théorique et Modélisation, <a href="https://ror.org/043htjv09">CY Cergy Paris Université</a>, CNRS, F-95302 Cergy-Pontoise, France.
Phys Rev Lett. 2024 Jul 5;133(1):010602. doi: 10.1103/PhysRevLett.133.010602.
We present a novel classical algorithm designed to learn the stabilizer group-namely, the group of Pauli strings for which a state is a ±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∼10^{3}. Our method, thanks to a very favorable scaling 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.
我们提出了一种新颖的经典算法，旨在学习给定矩阵乘积态（MPS）的稳定器群，即状态为±1本征向量的泡利字符串群。该算法基于泡利（或贝尔）基下巧妙且有理论依据的有偏采样。其输出是一组独立的稳定器生成元，其总数与稳定器零度直接相关，特别是一种成熟的非稳定器单调量。我们通过克利福德幺正动力学对随机加扰的T掺杂态进行方法基准测试，证明对于高达具有键维度χ∼10³的高度纠缠MPS，估计非常准确。我们的方法由于具有非常有利的O(χ³)缩放比例，代表了获得MPS真正魔法单调量的第一种有效方法，能够对非平衡态的量子多体物理进行系统研究。
