Highorder quantum algorithm for solving linear differential equations
Abstract
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of highorder methods to improve the efficiency. These provide scaling close to $\Delta t^2$ in the evolution time $\Delta t$. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution.
 Publication:

arXiv eprints
 Pub Date:
 October 2010
 DOI:
 10.48550/arXiv.1010.2745
 arXiv:
 arXiv:1010.2745
 Bibcode:
 2010arXiv1010.2745B
 Keywords:

 Quantum Physics;
 Computer Science  Numerical Analysis;
 Mathematics  Numerical Analysis
 EPrint:
 14 pages, improved efficiency