Block encodings and polynomials: a modern toolkit for quantum algorithms

par Pierre-Antoine Bernard (University of Toronto)

jeudi 22 oct. 2026, 11:00 → 12:00 Europe/Paris

Auditorium Vivargent (LAPTh)

Quantum computing has advanced rapidly in recent years, on both the hardware and the algorithmic fronts. On the algorithmic side, the past decade has brought a systematic way to translate linear algebra and functions of matrices into quantum circuits, making algorithm design more constructive and less reliant on intuition. At the heart of this approach are block encodings, which embed arbitrary matrices into unitary operations, and quantum signal processing (QSP), which applies polynomial transformations to them. Together they yielded an optimal algorithm for Hamiltonian simulation and a framework that unifies most known quantum algorithms. Extending these primitives is now central to the development of new quantum algorithms. In this talk, I will review this modern, block-encoding-based approach to quantum algorithms and its key techniques, including linear combinations of unitaries (LCU) and QSP. I will then discuss open questions about multivariate generalizations of QSP and their connections to classical results from the theory of orthogonal polynomials.