Quantum simulation of partial differential equations via Schrodingerisation: technical details
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arXiv
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| Natura: | Preprint |
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2022
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| _version_ | 1866913799740588032 |
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| author | Jin, Shi Liu, Nana Yu, Yue |
| author_facet | Jin, Shi Liu, Nana Yu, Yue |
| contents | We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential equations into a `Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation. Here we provide more in-depth technical discussions and expand on this approach in a more detailed and pedagogical way. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations. This approach can also be extended to Schrodingerise general linear partial differential equations, including the Vlasov-Fokker-Planck equation and the Liouville representation equation for nonlinear ordinary differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14703 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum simulation of partial differential equations via Schrodingerisation: technical details Jin, Shi Liu, Nana Yu, Yue Quantum Physics We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential equations into a `Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation. Here we provide more in-depth technical discussions and expand on this approach in a more detailed and pedagogical way. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations. This approach can also be extended to Schrodingerise general linear partial differential equations, including the Vlasov-Fokker-Planck equation and the Liouville representation equation for nonlinear ordinary differential equations. |
| title | Quantum simulation of partial differential equations via Schrodingerisation: technical details |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.14703 |