Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On models of nonlinear evolution paths in adiabatic quantum algorithms   In this paper, we study two different nonlinear interpolating paths in
adiabatic evolution algorithms for solving a particular class of quantum search
problems where both the initial and final Hamiltonian are one-dimensional
projector Hamiltonians on the corresponding ground state. If the overlap
between the initial state and final state of the quantum system is not equal to
zero, both of these models can provide a constant time speedup over the usual
adiabatic algorithms by increasing some another corresponding "complexity". But
when the initial state has a zero overlap with the solution state in the
problem, the second model leads to an infinite time complexity of the algorithm
for whatever interpolating functions being applied while the first one can
still provide a constant running time. However, inspired by a related
reference, a variant of the first model can be constructed which also fails for
the problem when the overlap is exactly equal to zero if we want to make up the
"intrinsic" fault of the second model-an increase in energy. Two concrete
theorems are given to serve as explanations why neither of these two models can
improve the usual adiabatic evolution algorithms for the phenomenon above.
These just tell us what should be noted when using certain nonlinear evolution
paths in adiabatic quantum algorithms for some special kind of problems.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
16
The categories of this paper are: stat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an