Quantum Signal Processing and Optimal Hamiltonian Simulation using Rydberg Atoms

Quantum algorithms promise an immense improvement to our current information processing capabilities by utilizing interference phenomena in an large Hilbert space. However, the large size of the Hilbert space also poses a crucial challenge to the experimentalists, who strive to design protocols that navigate the Hilbert space using only a small number of semiclassical control fields. Here, we design a set of multi-qubit Rydberg blockade gates that provide a solution to this control challenge. These gates are inspired by the recent developments in Quantum Signal Processing (QSP), a framework that unifies a vast number of quantum algorithms. We show that the proposed blockade gates facilitate a (i) robust (ii) shallow depth and (iii) scalable implementation of the so-called block-encoding unitary, the building block of the QSP framework. To showcase our approach, we construct explicit blueprints to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. Our protocols improve the gate overhead for implementing the product formula-based near-optimal simulation algorithm by more than an order of magnitude.