On the efficiency of Hamiltonian-based quantum computation for low-rank matrices

Zhenwei Cao, Alexander Elgart

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We present an extension of adiabatic quantum computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting subroutine. Our other results include a lower bound on the amount of time needed to perform a general Hamiltonian-based quantum search, a lower bound on the evolution time needed to perform a search that is valid in the presence of control error and a generic upper bound on the minimum eigenvalue gap for evolutions. In particular, we demonstrate that quantum speedup for the unstructured search using AQC type algorithms may only be achieved under very rigid control precision requirements.

Original languageEnglish
Article number032201
JournalJournal of Mathematical Physics
Volume53
Issue number3
DOIs
StatePublished - 19 Mar 2012
Externally publishedYes

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