Mixing and localization in random time-periodic quantum circuits of Clifford unitaries
Mixing and localization in random time-periodic quantum circuits of Clifford unitaries
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DOI：
10.1063/5.0054863
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发表时间：
2020-07
影响因子：
1.3
通讯作者：
Tom Farshi;D. Toniolo;C. E. González-Guillén;Álvaro M. Alhambra;L. Masanes
中科院分区：
文献类型：
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作者：
Tom Farshi;D. Toniolo;C. E. González-Guillén;Álvaro M. Alhambra;L. Masanes
局部和时间周期动力学在多大程度上类似于随机酉？在目前的工作中，我们通过使用量子计算中的Clifford形式主义来解决这个问题。我们分析了一个具有无序的Floquet模型，其特征是一维空间上的一组局部、时间周期和随机量子电路。我们观察到演化算子在周期的半整数倍时具有额外的对称性。由此，我们证明了在置乱时间之后，即当任何初始扰动传播到整个系统时，当所有量子位都用泡利算子测量时，演化算子不能与（Haar）随机酉相区分。这种不可区分性随着时间的推移而降低，这与（时间依赖的）随机电路的研究情况形成鲜明对比。我们还证明了泡利算子的演化表现出一种混合形式。这些结果要求局部子系统的尺寸较大。在相反的状态下，我们的系统显示出一种新的定位形式，由有效的单侧壁的出现产生，这可以防止扰动在一个方向上穿过壁，而不是在另一个方向上。
How much do local and time-periodic dynamics resemble a random unitary? In the present work, we address this question by using the Clifford formalism from quantum computation. We analyze a Floquet model with disorder, characterized by a family of local, time-periodic, and random quantum circuits in one spatial dimension. We observe that the evolution operator enjoys an extra symmetry at times that are a half-integer multiple of the period. With this, we prove that after the scrambling time, namely, when any initial perturbation has propagated throughout the system, the evolution operator cannot be distinguished from a (Haar) random unitary when all qubits are measured with Pauli operators. This indistinguishability decreases as time goes on, which is in high contrast to the more studied case of (time-dependent) random circuits. We also prove that the evolution of Pauli operators displays a form of mixing. These results require the dimension of the local subsystem to be large. In the opposite regime, our system displays a novel form of localization, produced by the appearance of effective one-sided walls, which prevent perturbations from crossing the wall in one direction but not the other.