Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos

Understand

We investigate circuit complexity to characterize chaos in multiparticle quantum systems.

• In the process, we take a stride to analyze open quantum systems by using complexity.
• We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix by exploring different types of quantum circuits.
• Through explicit calculations on a toy model of two coupled harmonic oscillators, where one or both of the oscillators are inverted, we demonstrate that the evolution of complexity is a possible diagnostic of chaos.