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

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.

arXiv comment26 pages, 9 figures, references updated, clarifying text added

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• Spread Complexity and Topological Transitions in the Kitaev Chain
• A universal approach to Krylov State and Operator complexities
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
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