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arXiv · 2212.14703

Quantum simulation of partial differential equations via Schrodingerisation: technical details

Shi Jin·Nana Liu·Yue Yu
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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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Shi Jin, Nana Liu, Yue Yu. 2022-12-30. Quantum simulation of partial differential equations via Schrodingerisation: technical details. https://doi.org/10.1103/physreva.108.032603

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