标题： 弱测量量子电路中存在量子比特丢失时流向Nishimori普适类的流动 显示英文标题

标题： Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss

摘要： 在基于电路的量子态制备中，比特丢失和相干误差是电路的不完善之处，它们威胁着在某一阈值之上形成长程纠缠。 阈值处的临界理论是一种连续的纠缠转变，已知可以用一个(2+0)维非幺正共形场论来描述，对于某些电路的两种不完善之处，分别由渗流或Nishimori临界性描述。 在这里，我们研究了当这两种错误同时发生时的阈值行为，并表明，当远离投影稳定器测量的Clifford区域时，渗流临界点变得不稳定，临界理论流向Nishimori普适类。 我们通过绘制出两个双协议的纠缠相图来追踪这一临界重正化群（RG）交叉流，这两个协议通过恒定深度电路从母团簇态制备表面码或GHZ类猫态，参数为随机弱测量的概率和强度。 使用混合高斯费米子和张量网络/蒙特卡洛采样技术对超过百万量子比特的系统进行的大量数值模拟表明，从Clifford区域的无穷小偏离会导致在初始非幺正RG流中突然出现强烈的非单调纠缠增长。 我们认为，渗流和Nishimori不动点的标度维度谱都表现出多重分形性。 对于渗流，我们提供了精确的（非二次）多重分形指数谱，而对于Nishimori不动点，我们展示了五个表征多重分形性的领先指数的高精度数值结果。 显示英文摘要

摘要： In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford-regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network / Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly non-monotonic entanglement growth at the incipient non-unitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (non-quadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.