Iterative Schreiffer-Wolff Transformation (ISWT)

Expert Technique

The techniques discussed below require careful consideration of the symmetry of the quantum system under consideration.

This submodule contains the NPAD technique, which is an exact SWT at the level of couplings. We provide a general ExactIterativeSWT class interface. This interface provides the following methods:

• givens_rotation_matrix(): Create the Given’s rotation matrix.

• unitary_transformation(): \(UHU^\dagger\) for NPAD. May be generalized to time-dependent case.

• eliminate_coupling(): Eliminate a single coupling.

• eliminate_couplings(): Eliminate multiple couplings simultaneously.

• largest_couplings(): Obtain the largest couplings.

There are two subclasses implementing NPAD: NPADScipySparse and NPADCupySparse, owing to differences between the SciPy and CuPy sparse matrix/array API. They each implement a givens_rotation_matrix() method using the appropriate sparse matrix module, since these matrices are largely sparse (\(N+2\) nonzero elements for \(N\times N\) matrices). For the user, an NPAD(H) function is provided for convenience. This will return an object of the appropriate subclass based on the input array H.