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arXiv · 2510.04294

Filtered Quantum Phase Estimation

Gwonhak Lee·Minhyeok Kang·Jungsoo Hong·Stepan Fomichev·Joonsuk Huh
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Abstract

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.

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Gwonhak Lee, Minhyeok Kang, Jungsoo Hong, Stepan Fomichev, Joonsuk Huh. 2025-10-05. Filtered Quantum Phase Estimation. https://arxiv.org/abs/2510.04294

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