Communications in Mathematical Physics

, Volume 356, Issue 3, pp 1057–1081 | Cite as

Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision

  • Dominic W. Berry
  • Andrew M. Childs
  • Aaron Ostrander
  • Guoming Wang


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.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Dominic W. Berry
    • 1
  • Andrew M. Childs
    • 2
    • 3
  • Aaron Ostrander
    • 3
    • 4
  • Guoming Wang
    • 3
  1. 1.Department of Physics and AstronomyMacquarie UniversitySydneyAustralia
  2. 2.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  3. 3.Joint Center for Quantum Information and Computer ScienceUniversity of MarylandCollege ParkUSA
  4. 4.Department of PhysicsUniversity of MarylandCollege ParkUSA

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