QSVT and QSVT_inversion

[MatP1337]

This PR implements Quantum Singular Value Transformation (QSVT). Additionally, it implements specialized function for matrix inversion, acting as a QLSP solver. QSP angles are obtained by utilizing the pyqsp library.

QSVT:

• inner_QSVT: Core QSVT circuit construction applying alternating phase modulated reflection and block-encoding unitaries according to the QSVT framework.
• inner_QSVT_wrapper: A repeat-until-success (RUS) decorated wrapper.
• QSVT: Simplified user-facing function wrapping the entire QSVT inversion workflow, supporting input matrix or it block-encoding tuple.

QSVT for matrix inversion and solving QLSP:

• inner_QSVT_inversion: Constructs QSVT circuits approximating matrix inversion with polynomial phase angles generated by the pyqsp library, supporting both Hermitian matrix input and explicit block-encoding tuples.
• inner_QSVT_inversion_wrapper: A repeat-until-success (RUS) decorated wrapper.
• QSVT_inversion: Simplified user-facing function wrapping the entire QSVT inversion workflow, supporting input matrix or it block-encoding tuple.

To-do:

• inner_QSVT:
  • make it possible to pass either the QSVT angles, or the desired polynomial (and compute angles within using pyqsp).
  • example with post-selection, without RUS (see inner_CKS)
• inner_QSVT_wrapper
• QSVT:
  • test if it works for matrix inversion
  • test if it works with QSVT angles for another matrix function
  • make it possible to pass either the QSVT angles, or the desired polynomial (and compute angles within using pyqsp).
  • docstring
    • examples
• tests