Dear friends, On Monday 23.06 at 11:00 in D5.01 we'll have a talk by Lorenzo Laneve about quantum signal processing. Title and abstract below. Join us in person or online at https://meet.jit.si/CQISeminarTalks Best regards, Will Schober Speaker: Lorenzo Laneve Title: An adversary bound for quantum signal processing Abstract: Quantum signal processing (QSP) is a technique that revolutionized quantum algorithmic theory: many new and known quantum algorithms — amplitude amplification, Hamiltonian simulation, and phase estimation — can be rewritten as the application of a polynomial transformation to the eigenvalue or singular values of a matrix that is block-encoded (e.g. the top-left block) in a unitary. A central question is to understand which polynomials we can achieve with QSP, especially when we have multiple signals. For this work, we borrow tools from quantum query complexity, namely state conversion and the adversary bound: we show that QSP can be seen as an instance of state conversion over the Hilbert space L^2 of square-integrable functions. As a consequence, the adversary bound is a semidefinite program that identifies all the possible QSP protocols for a desired transformation, even in the case of multiple variables, which constitutes an operational way to compute and test the existence of such protocols.