Filtered Quantum Phase Estimation
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914076213379072 |
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| author | Lee, Gwonhak Kang, Minhyeok Hong, Jungsoo Fomichev, Stepan Huh, Joonsuk |
| author_facet | Lee, Gwonhak Kang, Minhyeok Hong, Jungsoo Fomichev, Stepan Huh, Joonsuk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Filtered Quantum Phase Estimation Lee, Gwonhak Kang, Minhyeok Hong, Jungsoo Fomichev, Stepan Huh, Joonsuk Quantum Physics Computational Physics 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. |
| title | Filtered Quantum Phase Estimation |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2510.04294 |