The entanglement level statistics of a quantum state have recently been proposed to be a signature of universality in the underlying quantum circuit. This is a consequence of level repulsion in the entanglement spectra being tied to the integrability of entanglement generated. However, such studies of the level-spacing statistics in the entanglement spectrum have thus far been limited to the output states of Clifford and Haar random circuits on product state inputs. In this work, we provide the first example of a circuit which is composed of a simulable gate set, yet has a Wigner-Dyson distributed entanglement level spectrum without any perturbing universal element. We first show that, for matchgate circuits acting on random product states, Wigner-Dyson statistics emerge by virtue of a single SWAP gate, in direct analog to previous studies on Clifford circuits. We then examine the entanglement spectrum of matchgate circuits with varied input states, and find a sharp jump in the complexity of entanglement as we go from two- to three-qubit entangled inputs. Studying Clifford and matchgate hybrid circuits, we find examples of classically simulable circuits whose output states exhibit Wigner-Dyson entanglement level statistics in the absence of universal quantum gate elements. Our study thus provides strong evidence that entanglement spectrum is not strongly connected to notions of simulability in any given quantum circuit.

中文翻译：

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具有通用和非通用资源的匹配门电路的纠缠谱


最近，量子态的纠缠能级统计被认为是底层量子电路中普遍性的标志。这是纠缠谱中能级排斥力与所生成的纠缠的可积性相关的结果。然而，迄今为止，对纠缠谱中能级间距统计的此类研究仅限于乘积状态输入上的 Clifford 和 Haar 随机电路的输出状态。在这项工作中，我们提供了第一个由可模拟门组组成的电路示例，但具有维格纳-戴森分布纠缠能级谱，没有任何扰动通用元素。我们首先表明，对于作用于随机乘积状态的匹配门电路，维格纳-戴森统计通过单个交换门出现，与之前对克利福德电路的研究直接模拟。然后，我们检查具有不同输入状态的匹配门电路的纠缠谱，并发现当我们从两个量子位纠缠输入变为三个量子位纠缠输入时，纠缠的复杂性急剧上升。通过研究克利福德和匹配门混合电路，我们发现了经典可模拟电路的示例，其输出状态在没有通用量子门元件的情况下表现出维格纳-戴森纠缠级统计。因此，我们的研究提供了强有力的证据，表明纠缠谱与任何给定量子电路中的可模拟性概念没有紧密联系。