Primordial Gravitational Wave Circuit Complexity

Abstract

In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas models, etc. We compute complexity measures using both Covariance and Nielsen’s wave function method for three different choices of quantum initial vacua: Motta-Allen, α and Bunch–Davies. Besides computing circuit complexity, we also compute the Von Neumann entanglement entropy. By making the comparison between complexity and entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen’s measure of complexity, which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features on a cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute the quantum Lyapunov exponent for various cosmological models and comment on its chaotic nature.