复杂性第一定律The First Law of Complexity
Aspects of The First Law of Complexity
摘要：
我们研究了arXiv：1903.04511中提出的复杂性第一定律，即，当目标状态被扰动时复杂度的变化。基于Nielsen对量子线路复杂性的几何方法，我们发现这种变化只依赖于最优线路的末端。我们应用第一定律，以获得新的见解的量子线路和复杂性模型背后的全息复杂性。特别是，我们研究的变化的全息复杂性的复杂性=行动和复杂性=体积结构在扰动的AdS真空与相干态激发的自由标量场。我们还研究了电路复杂性的变化所产生的相同的激励的自由标量场理论在一个固定的AdS背景。在这种情况下，我们的工作扩展了现有的治疗高斯相干态，适当地包括复杂性变化的时间依赖性。我们评论的相似性和差异的全息和QFT的结果。
英文摘要：
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.
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