Quantum Circuit Complexity of Primordial Perturbations

TL;DR

This paper analyzes the quantum circuit complexity of cosmological perturbations across various early universe models, revealing differences in complexity growth and sensitivity to initial conditions.

Contribution

It introduces a symplectic group-based measure of complexity for cosmological perturbations and compares complexity evolution in different cosmological scenarios.

Findings

Inflationary perturbations have relatively simple quantum circuits.

Matter-dominated contraction leads to rapid complexity growth.

Ekpyrotic perturbations show minimal complexity growth.

Abstract

We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. A natural measure for the complexity of cosmological perturbations is based on the symplectic group, allowing us to identify complexity with geodesics in the hyperbolic plane. We investigate the complexity of both the mode functions and the physical perturbations, arguing that the latter often provides a more insightful description of the physics involved. In all models the total complexity reached is rather large. Inflationary perturbations may be represented by a comparatively simple quantum circuit, while the perturbations during a matter-dominated contracting phase present the most rapid growth in complexity. Ekpyrotic perturbations reside in the middle and are distinguished by the smallest growth of complexity before horizon exit. Our analysis serves to highlight how different cosmological models achieve the same end result for the perturbations via different routes and how all models show a pronounced sensitivity to initial conditions.