Quantum circuits for partial differential equations in Fourier space
Year: 2025
Type: article
Abstract: 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.
Source: Physical Review Research
DOI: 10.1103/tbzc-w9x8
Authors: Michael Lubasch, Yuta Kikuchi, Lewis Wright, Conor Mc Keever
Institutions: Quantinuum (United Kingdom), Quantinuum (United States), RIKEN
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
OpenAlex ID: W4417267522