Communications in Mathematical Physics

, Volume 270, Issue 2, pp 359–371

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

  • Dominic W. Berry
  • Graeme Ahokas
  • Richard Cleve
  • Barry C. Sanders
Article

DOI: 10.1007/s00220-006-0150-x

Cite this article as:
Berry, D.W., Ahokas, G., Cleve, R. et al. Commun. Math. Phys. (2007) 270: 359. doi:10.1007/s00220-006-0150-x

Abstract

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log*n)t1+1/2k) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Dominic W. Berry
    • 1
    • 2
  • Graeme Ahokas
    • 2
    • 3
  • Richard Cleve
    • 2
    • 3
    • 4
    • 5
  • Barry C. Sanders
    • 2
    • 6
  1. 1.Department of PhysicsThe University of QueenslandQueenslandAustralia
  2. 2.Institute for Quantum Information ScienceUniversity of CalgaryAlbertaCanada
  3. 3.Department of Computer ScienceUniversity of CalgaryAlbertaCanada
  4. 4.School of Computer ScienceUniversity of WaterlooOntarioCanada
  5. 5.Institute for Quantum ComputingUniversity of WaterlooOntarioCanada
  6. 6.Centre for Quantum Computer TechnologyMacquarie UniversitySydneyAustralia

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