Primordial Gravitational Wave Circuit Complexity

TL;DR

This paper explores quantum circuit complexity of primordial gravitational waves across various cosmological models, comparing it with entanglement entropy to understand quantum dynamics and chaos in the early universe.

Contribution

It introduces a comprehensive analysis of quantum circuit complexity in cosmology using multiple methods and initial vacua, linking complexity growth to chaotic behavior and quantum features.

Findings

Complexity varies across cosmological models.

Complexity growth correlates with chaotic dynamics.

Comparison with entanglement entropy reveals new insights.

Abstract

In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement entropy, and complexity are playing a pivotal role to understand the dynamics of quantum system even in the diverse fields such as, high energy physics and cosmology. This paper is devoted in studying quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas model etc. We compute complexity measure using both Covariance and Nielsen's wave function method for three different choices of quantum initial vacua: Motta-Allen, $\alpha$ and Bunch-Davies. Besides computing circuit complexity, we have also computed Von-Neumann entanglement entropy. By making the comparison of complexity with 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 in 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 quantum Lyapunov exponent for various cosmological models and comment on it's chaotic nature.