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  • Open Access

Function extraction via Chebyshev interpolation of quantum integral estimates

Gumaro Rendón*

  • *Contact author: grendon@fujitsu.com
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Phys. Rev. Research 8, 023095 – Published 30 April, 2026

DOI: https://doi.org/10.1103/r6xs-236q

Abstract

We present an algorithm for extracting a smooth, positive-definite function ψ(x) encoded in a quantum state vector of size 2n, while avoiding exponentially suppressed subnormalization of a naive extraction step. The method addresses a known limitation in quantum algorithms for differential equations, namely, the efficient retrieval of classical information from quantum-encoded solutions. It applies to settings where the target solution is smooth and positive definite, such as certain instances of the heat equation and related diffusive models arising in fluid dynamics and finance.

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Phys. Rev. Research 8, 023095– Published 30 April, 2026
  • Received 11 August 2025
  • Accepted 23 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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