Motivated by recent interesting holographic results, several attempts have been made to study complexity (rather “Circuit Complexity”) for quantum field theories using Nielsen’s geometric method. Since then, it has found many interesting applications. We discuss some of its applications. In particular, we discuss whether circuit complexity can be used as a diagnostics of quantum chaos. We use a simple toy model, namely the Inverted Harmonic Oscillator (IHO), to establish our claim and discuss further applications in the context of quantum cosmology.

中文翻译：

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电路复杂性及其（部分）应用

受最近有趣的全息结果的启发，已经进行了几次尝试，以使用 Nielsen 的几何方法研究量子场理论的复杂性（更确切地说是“电路复杂性”）。从那时起，它发现了许多有趣的应用。我们讨论了它的一些应用。特别是，我们讨论了电路复杂性是否可以用作量子混沌的诊断。我们使用一个简单的玩具模型，即反谐波振荡器 (IHO)，来确立我们的主张并讨论在量子宇宙学背景下的进一步应用。