Pierre-Antoine Bernard (University of Toronto)
Title:聽Quantum Signal Processing and orthogonal polynomials.
Abstract:聽Block encoding has emerged as a powerful unifying framework in quantum algorithms. By leveraging ancillary qubits and post-selection, it enables the implementation of non-unitary linear transformations within an overall unitary circuit. Methods such as Quantum Signal Processing (QSP), which aim to block-encode polynomials of a unitary operator, play a central role in Hamiltonian simulation and related applications. In this talk, I will review these techniques and propose a perspective in which they implement a block encoding of an entire polynomial basis, rather than a single polynomial. This viewpoint leads to a natural connection with the theory of orthogonal and biorthogonal polynomials, and allows for a structural characterization of the underlying polynomial families. Finally, I will discuss how this framework can be leveraged to address some limitations of QSP, including angle preprocessing and multivariate generalizations.
Location:聽Hybride Pav. Andr茅 Aisenstadt, salle/room 4336-4384聽
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