Quantum State-Aware Query Complexity: Krylov Compression and Polynomial Query Duality

• URL: http://arxiv.org/abs/2510.11786v1
• Date: Mon, 13 Oct 2025 18:00:03 GMT
• Title: Quantum State-Aware Query Complexity: Krylov Compression and Polynomial Query Duality
• Abstract summary: This state-aware perspective refines the worst-case bounds, Krylov/Favard approximation with quantum queries, and explains how state-dependent spectral structure can yield substantial savings over uniform designs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the minimal query complexity for preparing $f(H)\ket{\psi_0}$ is exactly the optimal polynomial approximation degree of $f$ in $L^2(\mu)$, where $\mu$ is the spectral measure of $(H,\ket{\psi_0})$. 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.

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