Towards a Geometrization of Quantum Complexity and Chaos

TL;DR

This paper explores how the Quantum Geometric Tensor, when restricted to locally generated states, offers new insights into quantum complexity, chaos, and phase transitions through a geometric perspective.

Contribution

It introduces a novel approach to geometrize quantum chaos and complexity using the Quantum Geometric Tensor restricted to local interaction manifolds.

Findings

Extension of quantum phase transition geometry out-of-equilibrium

Potential of Quantum Geometric Tensor to analyze quantum chaos

Framework for understanding locality effects in quantum complexity

Abstract

In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of a first result in this context, consisting in a geometric out-of-equilibrium extension of the quantum phase transitions, we argue the opportunity and the usefulness to exploit the Quantum Geometric Tensor to geometrize quantum chaos and complexity.