



01429nas a2200169   4500008004100000245010800041210006900149260001500218300001400233490000800247520088200255100002301137700002301160700002101183700001801204856003701222       2017                        eng d00aQuantum algorithm for linear differential equations with exponentially improved dependence on precision0 aQuantum algorithm for linear differential equations with exponen  c2017/12/01  a1057-10810 v3563 a<p><span style="font-family: &quot;Lucida Grande&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.</span></p>1 aBerry, Dominic, W.1 aChilds, Andrew, M.1 aOstrander, Aaron1 aWang, Guoming  uhttps://arxiv.org/abs/1701.03684