论文标题
随机矩阵产品状态的魔法
Magic of Random Matrix Product States
论文作者
论文摘要
魔术或非稳定器表征了一个州与稳定器状态相距多远，这使其成为量子计算的重要资源，在Gotteman-Knill定理的形式下。在本文中，我们使用$ L_ {1} $ - NORM MEATER研究了$ 1 $维的随机矩阵产品状态（RMPSS）的魔法。我们首先将$ l_ {1} $ - 标准与$ l_ {4} $ - norm相关联。然后，我们使用统一的$ 4 $ -DESIGN来将$ L_ {4} $ - 标准映射到$ 24 $ -COMPONENT统计物理模型。通过评估模型的分区函数，我们获得了$ L_ {1} $ - NORM的期望值的下限。这种界限相对于Qudit Number $ n $呈指数增长，这表明$ 1 $ d RMPS是高度神奇的。我们的数值结果证实了魔术在量子案例中呈指数增长。
Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the $1$-dimensional Random Matrix Product States (RMPSs) using the $L_{1}$-norm measure. We firstly relate the $L_{1}$-norm to the $L_{4}$-norm. We then employ a unitary $4$-design to map the $L_{4}$-norm to a $24$-component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the $L_{1}$-norm. This bound grows exponentially with respect to the qudit number $n$, indicating that the $1$D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case.
