论文标题
相互作用理论的扰动复杂性
Perturbative Complexity of Interacting Theory
论文作者
论文摘要
我们提出了一种系统的方法，可以在一系列耦合常数中扩展相互作用理论的量子复杂性。复杂性是通过操作员方法评估的，在该操作员方法中，参考状态的第二个量化运算符和目标状态的转换矩阵定义了量子门。我们从两个耦合振荡器开始，并扰动地评估了栅极基质相关组歧管的大地长度。接下来，我们将分析概括为$ n $耦合的振荡器，该振荡器描述了晶格$ λϕ^4 $理论。特别是，我们介绍简单的图表来表示扰动系列并构建简单的规则以有效计算复杂性。对于激发态的高阶复杂性，获得了一般公式。我们提供了几个图表来阐明复杂性的特性，并表明对复杂性的相互作用校正可能是正面的或负面的，具体取决于参考状态频率的大小。
We present a systematic method to expand the quantum complexity of interacting theory in series of coupling constant. The complexity is evaluated by the operator approach in which the transformation matrix between the second quantization operators of reference state and the target state defines the quantum gate. We start with two coupled oscillators and perturbatively evaluate the geodesic length of the associated group manifold of gate matrix. Next, we generalize the analysis to $N$ coupled oscillators which describes the lattice $λϕ^4$ theory. Especially, we introduce simple diagrams to represent the perturbative series and construct simple rules to efficiently calculate the complexity. General formulae are obtained for the higher-order complexity of excited states. We present several diagrams to illuminate the properties of complexity and show that the interaction correction to complexity may be positive or negative depending on the magnitude of reference-state frequency.
