Quantum signal processing with continuous variables

Understand

Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most quantum algorithms.

• QSVT depends on precise results in representation theory, with the desired polynomial functions acting simultaneously within invariant two-dimensional subspaces of a larger Hilbert space.
• These two-dimensional transformations are largely determined by the related theory of quantum signal processing (QSP).
• While QSP appears to rely on properties specific to the compact Lie group SU(2), many other Lie groups appear naturally in physical systems relevant to quantum information.