Quantum simulation of Burgers turbulence: Nonlinear transformation and direct evaluation of statistical quantities

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Pubblicato in:	arXiv.org (Dec 23, 2024), p. n/a
Autore principale:	Uchida, Fumio
Altri autori:	Miyamoto, Koichi, Yamazaki, Soichiro, Fujisawa, Kotaro, Yoshida, Naoki
Pubblicazione:	Cornell University Library, arXiv.org
Soggetti:	Transformations (mathematics) Quantum computing Technology assessment Quantum computers Finite difference method Fault tolerance Partial differential equations Fluid flow Algorithms Velocity distribution Fluid dynamics Burgers equation Nonlinear equations Nonlinear dynamics
Accesso online:	Citation/Abstract Full text outside of ProQuest
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Descrizione
Abstract:	Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the Burgers equation, using quantum computers. We propose a novel quantum algorithm to solve the Burgers equation. With the Cole-Hopf transformation that maps the fluid velocity field \(u\) to a new field \(\psi\), we apply a sequence of quantum gates to solve the resulting linear equation and obtain the quantum state \(\vert\psi\rangle\) that encodes the solution \(\psi\). We also propose an efficient way to extract stochastic properties of \(u\), namely the multi-point functions of \(u\), from the quantum state of \(\vert\psi\rangle\). Our algorithm offers an exponential advantage over the classical finite difference method in terms of the number of spatial grids when a perturbativity condition in the information-extracting step is met.
ISSN:	2331-8422
Fonte:	Engineering Database