Hi,

I would like to clarify the following code that was used to implement geometric difference from the paper: "The power of data in quantum machine learning".

def calculate_geometric_difference(k_1, k_2, normalization_lambda=0.001):
"""
Calculate the geometric difference g(K_1 || K_2), which is equation F9 in
"The power of data in quantum machine learning" (https://arxiv.org/abs/2011.01938)
and characterize the separation between classical and quantum kernels.
Args:
k_1: Quantum kernel Gram matrix
k_2: Classical kernel Gram matrix
normalization_lambda: normalization factor, must be close to zero
Returns:
geometric difference between the two kernel functions (float).
"""

In the paper, geometric difference between classical and quantum (g_cq ) is defined with k₁ = classical kernel and k₂ = quantum kernel. However, in your code implementation, k₁ is quantum and k₂ is classical. As the equation is asymmetric to the order of the matrices k₁ and k₂, could there be an error in the code implementation?

Thanks for taking the time to read this!