Nonuniversal entanglement level statistics in projection-driven quantum circuits
Nonuniversal entanglement level statistics in projection-driven quantum circuits
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DOI：
10.1103/physrevb.101.235104
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发表时间：
2020-01
影响因子：
3.7
通讯作者：
Lei Zhang;J. Reyes;S. Kourtis;C. Chamon;E. Mucciolo;A. Ruckenstein
中科院分区：
文献类型：
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作者：
Lei Zhang;J. Reyes;S. Kourtis;C. Chamon;E. Mucciolo;A. Ruckenstein
我们研究随机通用量子电路输出状态的纠缠谱中的能级间距统计，其中量子位在每个时间步都受到投影到计算基础的有限概率的影响。随着投影率的增加，我们遇到了两个相变：第一个是在具有投影测量的量子电路中观察到的体积-面积定律转变；第二个将大投影测量速率下的纯泊松能级统计相与面积律相内纠缠谱中的剩余能级排斥状态分开，其特征是在维格纳-戴森分布和泊松分布之间插值的非通用能级间距统计。通过应用参考文献中介绍的张量网络收缩算法。 [1]对于电路时空，我们将第二个投影测量驱动的转变识别为纠缠键的渗流转变。在随机双量子位酉电路和通用门集电路（包括 Google 在其 Sycamore 电路中实现的门集）中都观察到了相同的行为。
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum within the area-law phase, characterized by non-universal level spacing statistics that interpolates between the Wigner-Dyson and Poisson distributions. By applying a tensor network contraction algorithm introduced in Ref. [1] to the circuit spacetime, we identify this second projective-measurement-driven transition as a percolation transition of entangled bonds. The same behavior is observed in both circuits of random two-qubit unitaries and circuits of universal gate sets, including the set implemented by Google in its Sycamore circuits.