# The quantum geometric tensor from generating functions

## TL;DR

This paper presents a novel generating function approach to compute the Quantum Geometric Tensor, including the Quantum Information Metric and Berry curvature, applicable to theories with arbitrary interactions, demonstrated on perturbed harmonic oscillators.

## Contribution

Introduces a new perturbative method using generating functions to calculate the Quantum Geometric Tensor for interacting theories.

## Key findings

- Effective computation of Quantum Information Metric and Berry curvature
- Application to harmonic oscillators with linear and quartic perturbations
- Method generalizes to arbitrary interaction Hamiltonians

## Abstract

We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The calculation uses the generating function method, and it is illustrated with the harmonic oscillator with a linear and a quartic perturbation.