Work

Nearly optimal polynomial approximations for the quantum singular value transform

Year: 2026

Type: preprint

Abstract: We introduce polynomial approximations of the even and odd step functions on the interval $[-1,1]$ with simple Chebyshev coefficients, making their numerical implementation straightforward. We derive rigorous error bounds and demonstrate that these polynomials are nearly optimal in the sense that their error deviates from the theoretically optimal error by a multiplicative factor that grows logarithmically with the polynomial order. From these polynomials, we derive related nearly optimal polynomial approximations that can be used to perform quantum phase estimation, linear amplitude amplification, eigenvalue thresholding, and other quantum algorithms using the quantum singular value transform.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.12190

Author: Rule, Evan

Institution: Los Alamos National Laboratory

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, National Nuclear Security Administration, Los Alamos National Laboratory

Awards: G1017065088, G1279347439, G450742849, G6410514744, G6563880843

OpenAlex ID: W7168359072

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