Variational quantum evolution equation solver.
Sci Rep
; 12(1): 10817, 2022 Jun 25.
Article
in En
| MEDLINE
| ID: mdl-35752702
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.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
Sci Rep
Year:
2022
Document type:
Article
Affiliation country:
Singapur