论文标题
可整合的无空间开放量子电路
Integrable nonunitary open quantum circuits
论文作者
论文摘要
我们通过具有假想的相互作用强度的哈伯德模型的Trotteratization，明确构建了可集成且强烈的耗散量子电路。为了证明可集成性，我们构建了一个不均匀的传输矩阵，可以从中衍生出保守的超级操作器电荷，尤其是电路的动态发电机。在显示了痕量保存和局部地图的完全阳性之后，我们将其重新解释为具有单位点dephasing的自由费米斯局部动力学的Kraus表示。通过将相互作用添加到局部相干动力学或删除dephasing来通过添加相互作用来破坏地图的集成性。特别是，即使是由本地自由屈光度单位的凸组合构建的电路也不是不可整合的。此外，该构建使我们能够明确构建属于不同非热对称类别的电路，这些电路的特征是转置下的行为而不是复杂的共轭。我们通过使用复杂的间距比来检查耗散电路的光谱统计量来确认我们的所有分析结果。
We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved superoperator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the local dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. In particular, even circuits built from convex combinations of local free-fermion unitaries are nonintegrable. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.
