论文标题
复杂性第一定律的各个方面
Aspects of The First Law of Complexity
论文作者
论文摘要
我们研究了ARXIV：1903.04511中提出的复杂性的第一定律，即，当目标状态受到扰动时，复杂性的变化，更详细。基于Nielsen的量子电路复杂性的几何方法，我们发现变化仅取决于最佳电路的末端。我们将第一定律应用于全息复杂性的量子电路和复杂性模型。特别是，我们检查了复杂性=动作和复杂性的全息复杂性的变化=体积=体积构想在扰动ADS真空的情况下使用自由标量场的相干态度激发。我们还研究了固定ADS背景中相同激励对自由标量场理论产生的电路复杂性的变化。在这种情况下，我们的工作扩展了高斯相干状态的现有处理，以正确地包括复杂性变化的时间依赖性。我们评论全息和QFT结果的相似性和差异。
We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.
