Quantum simulation of partial differential equations via Schrodingerisation: technical details

• URL: http://arxiv.org/abs/2212.14703v1
• Date: Fri, 30 Dec 2022 13:47:35 GMT
• Title: Quantum simulation of partial differential equations via Schrodingerisation: technical details
• Authors: Shi Jin, Nana Liu and Yue Yu
• Abstract summary: 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. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations.
• Score: 31.986350313948435
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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