Isospectral Twirling and Quantum Chaos.
Isospectral Twirling and Quantum Chaos.
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DOI：
10.3390/e23081073
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发表时间：
2021-08-19
期刊：
影响因子：
--
通讯作者：
Hamma A
中科院分区：
文献类型：
--
作者：
Leone L;Oliviero SFE;Hamma A
我们证明了量子混沌最重要的度量，例如帧势、置乱、洛施密特回波和乱序相关器（OTOC），可以通过等谱旋转的统一框架（即 k 重酉信道的哈尔平均值）来描述。我们表明，这样的度量总是可以以等谱旋转的期望值的形式表达。在文献中，量子混沌有时通过光谱进行研究，有时通过生成动力学的哈密顿量的特征向量进行研究。我们证明，借助这种技术，我们可以在可积哈密顿量和量子混沌哈密顿量之间平滑插值。与特征向量取自哈尔测度的哈密顿量不同，具有特征向量稳定态的哈密顿量的等谱旋转不具有混沌特征。例如，与通用资源相比，使用 Clifford 资源获得的 OTOC 会衰减到更高的值。通过用非 Clifford 资源掺杂哈密顿量，我们展示了一类可积模型和量子混沌之间 OTOC 行为的交叉。此外，利用随机矩阵理论，我们表明这些量子混沌的度量清楚地区分了与高斯酉系综（GUE）给出的混沌谱相对应的量子混沌探针的有限时间行为与泊松分布和高斯对角系综（GDE）给出的可积谱。
We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).
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