Generalized Quantum Signal Processing

Understand

Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent quantum algorithms.

• However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations.
• In this paper, we present a Generalized Quantum Signal Processing (GQSP) approach, employing general SU(2) rotations as our signal processing operators, rather than relying solely on rotations in a single basis.
• Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that $|P|\leq 1$, a restriction necessary due to the unitary nature of quantum computation.