论文标题
随机电路中的纯度衰减率不同
Purity decay rate in random circuits with different configurations of gates
论文作者
论文摘要
我们研究纯度衰减 - 两分纠缠的量度 - 在$ n $ Qubits的链条中，在最近的邻居随机两端统一门的各种几何形状的作用下。我们使用Markov链的平均纯度演变描述，使用进一步的减少来获得仅在$ n $中的多项式尺寸的传输矩阵。在大多数电路中，一个例外是砖壁配置，纯度在两个阶段中衰落到其渐近价值：最初的热力学上相关衰减持续到很长时间是$ \ \simλ_{\ simλ_{\ mathrm {eff}}^t $，带有$λ_{最终的渐近衰变由转移矩阵的第二大特征值$λ_2$给出。有效速率$λ_ {\ mathrm {eff}} $取决于两部分边界的位置以及应用门的几何形状。
We study purity decay -- a measure of bipartite entanglement -- in a chain of $n$ qubits under the action of various geometries of nearest-neighbor random two-site unitary gates. We use a Markov chain description of average purity evolution, using further reduction to obtain a transfer matrix of only polynomial dimension in $n$. In most circuits, an exception being the brick-wall configuration, purity decays to its asymptotic value in two stages: the initial thermodynamically relevant decay persisting up to extensive times is $\sim λ_{\mathrm{eff}}^t$, with $λ_{\mathrm{eff}}$ not necessarily being in the spectrum of the transfer matrix, while the ultimate asymptotic decay is given by the second largest eigenvalue $λ_2$ of the transfer matrix. The effective rate $λ_{\mathrm{eff}}$ depends on the location of bipartition boundaries as well as on the geometry of applied gates.
