Quantum Signal-Processing based Phase Estimation (QSPE) is a readily deployable quantum metrology technique that harnesses Quantum Signal Processing (QSP) and polynomial analysis to achieve Heisenberg-limit precision in one- and two-qubit systems using low-depth circuits, making it suitable for the NISQ era. QSP allows us to model input quantum signals to realize target quantum dynamics in the output through parameterized universal transformations on the input. QSPE separates the estimation of parameters free from time-dependent errors from those affected by time-dependent errors. Building on recent work [1] that enables in situ estimation of Hamiltonian parameters for multi-atom systems, we adapt these techniques to Rydberg-atom systems [2] with pulse-level control, achieving the Heisenberg limit and a framework robust to several realistic experimental noise sources.
[1] Y. Dong, J. A. Gross, and M. Y. Niu, Optimal low-depth quantum signal-processing phase estimation, Nat Commun 16, 1504 (2025).
[2] S. Liu, X. Wu, and M. Y. Niu, Optimal and Robust In-Situ Quantum Hamiltonian Learning through Parallelization, arXiv:2510.07818.