Quantum simulation of partial differential equations via Schrodingerisation: technical details
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
Shi Jin
Nana Liu
Yue Yu
Akses Cepat
- Tahun Terbit
- 2022
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓