



01292nas a2200145   4500008004100000245005600041210005600097260001400153300001400167490000800181520087900189100002301068700001801091856003701109       2020                        eng d00aQuantum spectral methods for differential equations0 aQuantum spectral methods for differential equations  c2/18/2020  a1427-14570 v3753 a<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>1 aChilds, Andrew, M.1 aLiu, Jin-Peng  uhttps://arxiv.org/abs/1901.00961