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.
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.