Nonstabilizerness, also known as “magic,” stands as a crucial resource for achieving a potential advantage in quantum computing. Its connection to many-body physical phenomena is poorly understood at present, mostly due to a lack of practical methods to compute it at large scales. We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPSs), based on expressing the MPS directly in the Pauli basis. Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer Rényi entropies, stabilizer nullity, and Bell magic, and enables the learning of the stabilizer group of an MPS. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays, where we provide concrete benchmarks for future experiments on logical qubits up to twice the sizes already realized.

中文翻译：

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通过泡利基础中的矩阵积状态的非稳定性


非稳定性，也称为“魔法”，是在量子计算中实现潜在优势的关键资源。目前人们对它与多体物理现象的联系知之甚少，主要是由于缺乏大规模计算它的实用方法。我们提出了一种在矩阵积态 (MPS) 框架内评估非稳定性的新方法，基于直接在泡利基中表达 MPS。我们的框架提供了一个强大的工具，可以有效地计算各种非稳定性度量，包括稳定器 Rényi 熵、稳定器无效性和贝尔魔力，并且能够学习 MPS 的稳定器组。我们展示了我们的方法在 Ising 和 XXZ 自旋链的基态以及最近在里德堡原子阵列中实现的电路动力学中的有效性和多功能性，其中我们为未来逻辑量子位的实验提供了具体的基准，最多可达两倍尺寸已经实现。