Simulating Hamiltonian Dynamics with a Truncated Taylor Series

Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma
Phys. Rev. Lett. 114, 090502 – Published 3 March 2015

Abstract

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

  • Received 16 December 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.090502

© 2015 American Physical Society

Authors & Affiliations

Dominic W. Berry1, Andrew M. Childs2,3,4,5, Richard Cleve2,5,6, Robin Kothari2,6,7, and Rolando D. Somma8

  • 1Department of Physics and Astronomy, Macquarie University, Sydney, New South Wales 2109, Australia
  • 2Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1, Canada
  • 3Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada
  • 4Department of Computer Science, Institute for Advanced Computer Studies, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20910, USA
  • 5Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
  • 6School of Computer Science, University of Waterloo, Ontario N2L 3G1, Canada
  • 7Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 8Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 114, Iss. 9 — 6 March 2015

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