Quantum circuits for partial differential equations in Fourier space

Fuente: arXiv
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Autores principales: Lubasch, Michael, Kikuchi, Yuta, Wright, Lewis, Keever, Conor Mc
Formato: Preprint
Publicado: 2025
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author Lubasch, Michael
Kikuchi, Yuta
Wright, Lewis
Keever, Conor Mc
author_facet Lubasch, Michael
Kikuchi, Yuta
Wright, Lewis
Keever, Conor Mc
contents For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements. This is shown by explicit circuit constructions for the incompressible advection, heat, isotropic acoustic wave, and Poisson's equations as canonical examples. We utilize quantum singular value transformation to develop circuits that are expected to be of optimal computational complexity. Additionally, we consider approximations suited for smooth initial conditions and describe circuits that make lower demands on hardware. The simple QFT-based circuits are efficient with respect to dimensionality and pave the way for current quantum computers to solve high-dimensional PDEs.
format Preprint
id arxiv_https___arxiv_org_abs_2505_16895
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantum circuits for partial differential equations in Fourier space
Lubasch, Michael
Kikuchi, Yuta
Wright, Lewis
Keever, Conor Mc
Quantum Physics
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements. This is shown by explicit circuit constructions for the incompressible advection, heat, isotropic acoustic wave, and Poisson's equations as canonical examples. We utilize quantum singular value transformation to develop circuits that are expected to be of optimal computational complexity. Additionally, we consider approximations suited for smooth initial conditions and describe circuits that make lower demands on hardware. The simple QFT-based circuits are efficient with respect to dimensionality and pave the way for current quantum computers to solve high-dimensional PDEs.
title Quantum circuits for partial differential equations in Fourier space
topic Quantum Physics
url https://arxiv.org/abs/2505.16895