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Quantum Optimization
Quantum Simulation
Krylov Polynomials and Quantum Query Complexity
arXiv
Authors: Kiran Adhikari
Year
2025
Paper ID
51277
Status
Preprint
Abstract Read
~2 min
Abstract Words
58
Citations
N/A
Abstract
We show that the minimal query complexity for preparing f(H)ket{ψ0} is exactly the optimal polynomial approximation degree of f in L2(μ), where μ is the spectral measure of \(H,ket{ψ0}\). 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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- We show that the minimal query complexity for preparing f(H)ketψ0 is exactly the optimal polynomial approximation degree of f in L^2(μ), where μ is the spectral measure of...
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