A spectral quantum algorithm for numerical differentiation and integration
- URL: http://arxiv.org/abs/2506.19959v1
- Date: Tue, 24 Jun 2025 19:11:52 GMT
- Title: A spectral quantum algorithm for numerical differentiation and integration
- Authors: Jordan Cioni, Fabio Semperlotti,
- Abstract summary: We present low-complexity quantum algorithms for numerical differentiation and integration in partially bounded domains.<n>The algorithms are based on a spectral approach that allows taking advantage of the computationally efficient quantum Fourier transform algorithm.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper presents low-complexity quantum algorithms for numerical differentiation and integration in partially bounded domains. The algorithms are based on a spectral approach that allows taking advantage of the computationally efficient quantum Fourier transform algorithm. Full derivations and gate-level circuit examples are presented. As part of the integration algorithms, we also develop an encoding technique to efficiently perform element-wise multiplication operations and unitary operators to perform partial summations of information encoded in state amplitudes.
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