Environment

• Qiskit version: 2.1
• Python version:
• Operating system:

What is happening?

Need to improve the tolerance of the cosine-sine decomposition in cos_sin_decomp.rs, which is used in the Quantum Shannon Decomposition (QSD).
As QSD is using the cosine-sine recursively, the tolerance errors are getting accumulated, especially when handling multi-controlled unitary operators, see the discussion in #13688, so in certain cases we should use the Isometry synthesis which requires more CX gates.
The current code for the cosine-sine decomposition is based on rust nalgebra SVD function.

How can we reproduce the issue?

see the discussion in #13688, call:
Operator(qsd.qs_decomposition(mat)) for certain matrices gives a matrix way different than the original mat

What should happen?

Operator(qsd.qs_decomposition(mat)) should give back mat up to a reasonable tolerance level

Any suggestions?

No response