Krylov Polynomials and Quantum Query Complexity

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1. Verfasser: Adhikari, Kiran
Format: Preprint
Veröffentlicht: 2025
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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