TY - JOUR T1 - Quantum algorithm for linear differential equations with exponentially improved dependence on precision JF - Communications in Mathematical Physics Y1 - 2017 A1 - Dominic W. Berry A1 - Andrew M. Childs A1 - Aaron Ostrander A1 - Guoming Wang AB -

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.

VL - 356 U4 - 1057-1081 UR - https://arxiv.org/abs/1701.03684 CP - 3 ER -