Article

Communications in Mathematical Physics

, Volume 270, Issue 2, pp 359-371

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

  • Dominic W. BerryAffiliated withDepartment of Physics, The University of QueenslandInstitute for Quantum Information Science, University of Calgary
  • , Graeme AhokasAffiliated withInstitute for Quantum Information Science, University of CalgaryDepartment of Computer Science, University of Calgary
  • , Richard CleveAffiliated withInstitute for Quantum Information Science, University of CalgaryDepartment of Computer Science, University of CalgarySchool of Computer Science, University of WaterlooInstitute for Quantum Computing, University of Waterloo
  • , Barry C. SandersAffiliated withInstitute for Quantum Information Science, University of CalgaryCentre for Quantum Computer Technology, Macquarie University

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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)t 1+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.