Quantum algorithm for linear differential equations with exponentially improved dependence on precision

Dominic W. Berry, Andrew M. Childs, Aaron Ostrander*, Guoming Wang

*Corresponding author for this work

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1057-1081
Number of pages25
JournalCommunications in Mathematical Physics
Volume356
Issue number3
DOIs
Publication statusPublished - 1 Dec 2017

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