Krylov Polynomials and Quantum Query Complexity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917115225702400 |
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| author | Adhikari, Kiran |
| author_facet | Adhikari, Kiran |
| contents | We show that the minimal query complexity for preparing $f(H)\ket{ψ_0}$ is exactly the optimal polynomial approximation degree of $f$ in $L^2(μ)$, where $μ$ is the spectral measure of $(H,\ket{ψ_0})$. This state-aware perspective refines the worst-case bounds, unifies Krylov/Favard approximation with quantum queries, and explains how state-dependent spectral structure can yield substantial savings over uniform designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Krylov Polynomials and Quantum Query Complexity Adhikari, Kiran Quantum Physics High Energy Physics - Theory We show that the minimal query complexity for preparing $f(H)\ket{ψ_0}$ is exactly the optimal polynomial approximation degree of $f$ in $L^2(μ)$, where $μ$ is the spectral measure of $(H,\ket{ψ_0})$. This state-aware perspective refines the worst-case bounds, unifies Krylov/Favard approximation with quantum queries, and explains how state-dependent spectral structure can yield substantial savings over uniform designs. |
| title | Krylov Polynomials and Quantum Query Complexity |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.11786 |