Variational quantum evolution equation solver
Abstrak
Abstract Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the Ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank–Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction–diffusion and the incompressible Navier–Stokes equations, and demonstrate its validity by proof-of-concept results.
Penulis (3)
Fong Yew Leong
Wei-Bin Ewe
Dax Enshan Koh
Akses Cepat
- Tahun Terbit
- 2022
- Sumber Database
- DOAJ
- DOI
- 10.1038/s41598-022-14906-3
- Akses
- Open Access ✓