Arbitrary response measurements via Quantum Signal Processing

The experimental platforms for quantum information conventionally offer only projective measurements on single qubits. Hence the realization of generalized measurements require the interaction between the system and an ancilla. Although a complete theoretical framework for such generalized measurements is in place, an explicit experimental protocol that allows the design of arbitrary measurement operators has so far been elusive. In this work, we show that combining Quantum Signal Processing (QSP) with many-body interferometry yields a vast library of protocols for measuring high-order space-,time-, and frequency-dependent response functions. We provide a detailed analysis of the implementation of our protocol in the Rydberg atom platform. Our work demonstrates the close relation between QSP and generalized measurements, and naturally yields a novel way of block-encoding arbitrary functions of Hamiltonians realized in Rydberg atom systems.