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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17206 |
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| _version_ | 1866915858041798656 |
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| author | Uchida, Fumio Miyamoto, Koichi Yamazaki, Soichiro Fujisawa, Kotaro Yoshida, Naoki |
| author_facet | Uchida, Fumio Miyamoto, Koichi Yamazaki, Soichiro Fujisawa, Kotaro Yoshida, Naoki |
| contents | 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 $ψ$, we apply a sequence of quantum gates to solve the resulting linear equation and obtain the quantum state $\vertψ\rangle$ that encodes the solution $ψ$. We also propose an efficient way to extract stochastic properties of $u$, namely the multi-point functions of $u$, from the quantum state of $\vertψ\rangle$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum simulation of Burgers turbulence: Nonlinear transformation and direct evaluation of statistical quantities Uchida, Fumio Miyamoto, Koichi Yamazaki, Soichiro Fujisawa, Kotaro Yoshida, Naoki Quantum Physics Fluid Dynamics 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 $ψ$, we apply a sequence of quantum gates to solve the resulting linear equation and obtain the quantum state $\vertψ\rangle$ that encodes the solution $ψ$. We also propose an efficient way to extract stochastic properties of $u$, namely the multi-point functions of $u$, from the quantum state of $\vertψ\rangle$. 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. |
| title | Quantum simulation of Burgers turbulence: Nonlinear transformation and direct evaluation of statistical quantities |
| topic | Quantum Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2412.17206 |