Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Gap Analysis for Efficient Tunneling in Quantum Adiabatic
  Optimization   We investigate the efficiency of Quantum Adiabatic Optimization when
overcoming potential barriers to get from a local to a global minimum.
Specifically we look at n qubit systems with symmetric cost functions f:{0,
1}^n->R where the ground state must tunnel through a potential barrier of width
n^a and height n^b. By the quantum adiabatic theorem the time delay sufficient
to ensure tunneling grows quadratically with the inverse spectral gap during
this tunneling process. We analyze barrier sizes with 1/2 < a + b and a < 1/2
and show that the minimum gap scales polynomially as n^{1/2-a-b} when 2a+b < 1
and exponentially as n^{-b/2} exp(-C n^{(2a+b-1)/2} ) when 1 < 2a+b. Our proof
uses elementary techniques and confirms and extends an unpublished folklore
result by Goldstone, which used large spin and instanton methods. Parts of our
result also refine recent results by Kong and Crosson and Jiang et al. about
the exponential gap scaling.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph