论文标题
（2+1）d监视的随机量子电路中的拓扑顺序和关键性
Topological order and criticality in (2+1)D monitored random quantum circuits
论文作者
论文摘要
最近发现，随机量子电路为实现丰富的纠缠相图提供了一条途径，这些途径被隐藏在运算符的标准期望值中。在这里，我们研究（2+1）D随机电路，具有随机的Clifford单一大门和旨在稳定琐碎区域定律和拓扑结构阶段的测量值。除了随机的Clifford单位外，我们还找到了一个涉及三个临界点的相图，该相位图涉及（2+1）d渗透，这是一个可能稳定的关键阶段，一个可能稳定的关键阶段，拓扑，拓扑，微不足道的，微不足道的，小数量和数量定律阶段和关键点的线路，我们找到了一个相图，我们找到了竞争性的单量子。相反，通过Pauli-Y单量子量子测量值，我们发现了一个各向异性的自与双重三级点点，动态指数$ z \约1.46 $，表现出对区域定律的对数违规和拓扑缠结熵的异常指数，因此从任何已知的percolation固定固定点上都显着。该相图还具有在没有统一动力学的情况下，具有测量诱导的体积定律纠缠的相位。
It has recently been discovered that random quantum circuits provide an avenue to realize rich entanglement phase diagrams, which are hidden to standard expectation values of operators. Here we study (2+1)D random circuits with random Clifford unitary gates and measurements designed to stabilize trivial area law and topologically ordered phases. With competing single qubit Pauli-Z and toric code stabilizer measurements, in addition to random Clifford unitaries, we find a phase diagram involving a tricritical point that maps to (2+1)D percolation, a possibly stable critical phase, topologically ordered, trivial, and volume law phases, and lines of critical points separating them. With Pauli-Y single qubit measurements instead, we find an anisotropic self-dual tricritical point, with dynamical exponent $z \approx 1.46$, exhibiting logarithmic violation of the area law and an anomalous exponent for the topological entanglement entropy, which thus appears distinct from any known percolation fixed point. The phase diagram also hosts a measurement-induced volume law entangled phase in the absence of unitary dynamics.
