Simulating quantum dynamics on a quantum computer

Nathan Wiebe*, Dominic W. Berry, Peter Høyer, Barry C. Sanders

*Corresponding author for this work

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We explicitly show how to simulate time-dependent sparse Hamiltonian evolution on a quantum computer, with complexity that is close to linear in the evolution time. The complexity also depends on the magnitude of the derivatives of the Hamiltonian. We propose a range of techniques to simulate Hamiltonians with badly behaved derivatives. These include using adaptive time steps, adapting the order of the integrators, and omitting regions about discontinuities. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian, and accounts for all computational resources. We explicitly determine the number of bits of output that this oracle needs to provide, and show how to efficiently perform the required 1-sparse unitary operations using these bits. We also account for discretization error in the time, as well as accounting for Hamiltonians that are a sum of terms that are sparse in different bases.

Original languageEnglish
Article number445308
Pages (from-to)1-27
Number of pages27
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number44
DOIs
Publication statusPublished - 4 Nov 2011
Externally publishedYes

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