Filtered Quantum Phase Estimation

Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground-state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap with the desired eigenstate remains a major challenge. To address this, we develop a unified cost-aware framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering. The framework covers polynomial and trigonometric realizations of filters and makes explicit the trade-off among overlap amplification, preparation success probability, and filter-implementation cost. As representative examples, we analyze Gaussian filters and introduce a modified Krylov-subspace-based filter that improves the success-probability/overlap trade-off relevant to filtered state preparation. Within this framework, we study a filtered variant of quantum phase estimation (FQPE) that mitigates the unfavorable dependence on the initial overlap present in standard QPE. Numerical experiments on Fermi–Hubbard models show that FQPE reduces the total runtime by more than two orders of magnitude in the high-precision regime, with overlap amplification exceeding a factor of one hundred.