Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the efficiency of Hamiltonian-based quantum computation for low-rank
  matrices   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.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg