TY - JOUR T1 - Quantum spectral methods for differential equations JF - Commun. Math. Phys. Y1 - 2020 A1 - Andrew M. Childs A1 - Jin-Peng Liu AB -

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)).

VL - 375 U4 - 1427-1457 UR - https://arxiv.org/abs/1901.00961 U5 - https://doi.org/10.1007/s00220-020-03699-z ER -