



@article {2333,
	title = {Quantum spectral methods for differential equations},
	journal = {Commun. Math. Phys. },
	volume = {375},
	year = {2020},
	month = {2/18/2020},
	pages = {1427-1457},
	abstract = {<p>Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ε with complexity poly(log(1/ε)), no such algorithm was previously known for differential equations with time-dependent coefficients. Here we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd,log(1/ε)).</p>},
	doi = {https://doi.org/10.1007/s00220-020-03699-z},
	url = {https://arxiv.org/abs/1901.00961},
	author = {Andrew M. Childs and Jin-Peng Liu}
}
