Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
Arpan Bhattacharyya, S. Shajidul Haque, Eugene H. Kim
TL;DR
This paper introduces a new complexity-based diagnostic for quantum chaos using reduced density matrices, demonstrated on a toy model of coupled oscillators, extending the analysis to open quantum systems.
Contribution
It proposes a novel chaos diagnostic based on complexity and reduced density matrices, applicable to open quantum systems and demonstrated through explicit calculations.
Findings
Complexity evolution correlates with chaos in the toy model.
The diagnostic works for different types of quantum circuits.
Open quantum systems can be analyzed using this complexity-based approach.
Abstract
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.
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