Input-to-state stability-based continualized quantum filtering for robust phase estimation

This paper presents a framework integrating input-to-state stability-based continualized quantum filtering with Kitaev’s quantum phase estimation to enable robust phase estimation within the Hilbert space of noisy intermediate-scale quantum systems. The approach employs a stochastic master equation to model quantum dynamics, combining quantum phase estimation phase encoding with continuous weak measurements and input-to-state stability analysis to ensure reliable estimation despite stochastic disturbances like measurement noise. Numerical simulations compare the performance of Kitaev’s quantum phase estimation and the input-to-state stability-filtered across Gaussian noise levels and under phase damping channel. Future work will focus on optimizing feedback control and validating on hardware to minimize numerical instability.