iqm.benchmarks.compressive_gst.mgst.optimization.tangent_proj

iqm.benchmarks.compressive_gst.mgst.optimization.tangent_proj(K: ndarray, Z: ndarray, d: int, rK: int) → ndarray

Projection onto the local tangent space.

Parameters:

• K (ndarray) – Current position

• Z (ndarray) – Element of the ambient space to be projected onto the tangent space at K

• d (int) – Number of matrices which are projected (i.e. number of gates in the gate set)

• rK (int) – Kraus rank of the gate set

Returns:

Projection of Z onto the tangent space of the Stiefel manifold at position K

Return type:

ndarray

Notes

The projection is done with respect to the canonical metrik.