论文标题
仅测量XZZX量子代码中的拓扑顺序和纠缠动态
Topological order and entanglement dynamics in the measurement-only XZZX quantum code
论文作者
论文摘要
我们检查了$（1+1）$ - 尺寸测量电路的动力学，这是由[[5,1,3]]量子误差的稳定器定义的，纠正了单位Pauli测量中断的代码。该代码纠正了任意的单量错误，并以$ D_2 = \ Mathbb {Z} _2 \ Times \ Times \ Mathbb {Z} _2 $对称性保护拓扑（SPT）顺序稳定区域法律，并从对称性（SB）订购（SB）。 Pauli的测量破坏了拓扑秩序，并引起了相位过渡到微不足道的法律阶段。允许多种类型的Pauli测量可以增加测量引起的挫败感，并且可以以非零的测量速率同时或分别折断SPT和SB顺序。在相变处，这产生了丰富的相图和意外的临界行为。尽管相关长度指数$ν= \ tfrac43 $和动态临界指数$ z = 1 $与债券渗透是一致的，但对数纠缠增长的预先成品可能需要渗透率的非直集倍数。值得注意的是，我们为$ l $ Qubits的纯化动力学确定了强大的瞬态缩放制度。它揭示了一个修改的动态关键指数$ z^*\ neq z $，直到可以观察到$ t \ sim l^{z^*} $，并且让人联想到关键系统放松到预先状态。
We examine the dynamics of a $(1+1)$-dimensional measurement-only circuit defined by the stabilizers of the [[5,1,3]] quantum error correcting code interrupted by single-qubit Pauli measurements. The code corrects arbitrary single-qubit errors and it stabilizes an area law entangled state with a $D_2 = \mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry protected topological (SPT) order, as well as a symmetry breaking (SB) order from a two-fold bulk degeneracy. The Pauli measurements break the topological order and induce a phase transition into a trivial area law phase. Allowing more than one type of Pauli measurement increases the measurement-induced frustration, and the SPT and SB order can be broken either simultaneously or separately at nonzero measurement rate. This yields a rich phase diagram and unanticipated critical behavior at the phase transitions. Although the correlation length exponent $ν=\tfrac43$ and the dynamical critical exponent $z=1$ are consistent with bond percolation, the prefactor of the logarithmic entanglement growth may take non-integer multiples of the percolation value. Remarkably, we identify a robust transient scaling regime for the purification dynamics of $L$ qubits. It reveals a modified dynamical critical exponent $z^*\neq z$, which is observable up to times $t\sim L^{z^*}$ and is reminiscent of the relaxation of critical systems into a prethermal state.
