Polynomial time constructive decision algorithm for multivariable quantum signal processing

Understand

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation.

• As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed.
• M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations.
• However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown.