Murphy Niu

Quantum Signal Processing (QSP) stands out for its ability to generate optimal or near-optimal quantum algorithms for linear algebra problems and quantum system simulation, while unifying diverse quantum algorithms under a single analytical framework. However, existing formulations assume fault-tolerant computation, limiting near-term applicability. In this work, we introduce two advances aimed at bridging this gap: Quantum Signal Processing Phase Estimation (QSPE) and Feedforward QSP. Our QSPE approach leverages QSP’s analytical structure to perform nonlinear transformations that dramatically improve the accuracy and efficiency of learning unitary gates and multi-qubit Hamiltonians—achieving, for the first time, the theoretical optimal bound for these tasks in practical demonstrations. Meanwhile, Feedforward QSP extends QSP by incorporating classical feedback from ancillary measurements, enabling the reutilization of quantum information typically lost during measurement. This integration enhances the efficiency of Quantum Singular Value Transformation (QSVT) circuits. Together, these techniques—combining error mitigation with classical feedforward—mark a key step toward realizing QSP’s full potential for near-term quantum applications.