Filtered Quantum Phase Estimation

• URL: http://arxiv.org/abs/2510.04294v1
• Date: Sun, 05 Oct 2025 17:11:30 GMT
• Title: Filtered Quantum Phase Estimation
• Abstract summary: We develop a unified framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering.<n>We further develop a filtered variant of QPE that mitigates the unfavorable dependence on the initial overlap present in standard QPE.<n>Experiments 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.
• Score: 2.6967769052209873
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 to the desired eigenstate remains a major challenge. To address this, we develop a unified framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering. This framework encompasses the polynomial and trigonometric realizations of filters, allowing a transparent analysis of the trade-offs between overlap amplification and preparation cost. As examples, we introduce signal-processing-inspired filters, such as Gaussian filters and Krylov subspace-based filters, that adaptively suppress excited-state contributions using low-rank projections. Within this framework, we further develop a filtered variant of QPE (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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