论文标题
热场动力学中广义相干状态的电路复杂性
Circuit complexity for generalised coherent states in thermal field dynamics
论文作者
论文摘要
在这项工作中，我们通过采用协方差矩阵方法来研究热系统中广义相干状态的电路复杂性。我们专注于相干的热（CT）状态，该状态是非高斯，具有非变化的一分函数。我们发现，即使CT状态不能由对称的两点函数完全确定，但仍可以通过适当扩大协方差矩阵来计算电路复杂性在协方差矩阵形式上。现在，统一产生的组是翻译和符号群的半副作用。如果参考状态是高斯，则最佳测量机构仍然由水平发电机生成，因此可以通过将成本函数为$ f_2 $从与目标状态相关的广义协方差矩阵中读取电路复杂性。对于单个谐波振荡器，我们在参考状态为高斯并且目标空间被单个模式或双模式激发的情况下仔细讨论复杂性及其形成。我们表明，该研究可以扩展到自由标量场理论。
In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be $F_2$. For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.
