Dear friends, Tomorrow at 15.30 in D0.02 Lorenzo will give a talk on some very recent ideas he's had about lower bounding the multivariate QSP protocol. Title and abstract below. Join us in person or online at https://meet.jit.si/CQISeminarTalks Oh, and don't miss Gilles Brassard's talk earlier in the day at 11 in D1.14! Warmly, Will Title: An adversary bound for multivariate quantum signal processing Abstract: Quantum signal processing (QSP) is a recent technique in the context of algorithmic design, which consists of realising polynomial transformations of a variable (the signal) embedded in a unitary operator (the signal operator). It can be shown that a QSP ansatz can achieve nearly any polynomial, up to clear and mild conditions. These techniques allow to unify a variety of known problems (including fixed-point amplitude amplification, phase estimation, and optimal Hamiltonian simulation), by simply defining a suitable polynomial transformation for the eigenvalues or singular values of a given matrix that is block-encoded in a quantum circuit. While the class of implementable polynomials is well-understood when the signal is a single variable, the case of multivariate signals is still open. In this work, we borrow tools from quantum query complexity (namely adversary method and gamma norms), to give a lower bound on the number of steps needed to implement a given multivariate polynomial.