Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum algorithm for finding the negative curvature direction in
  non-convex optimization   We present an efficient quantum algorithm aiming to find the negative
curvature direction for escaping the saddle point, which is the critical
subroutine for many second-order non-convex optimization algorithms. We prove
that our algorithm could produce the target state corresponding to the negative
curvature direction with query complexity O(polylog(d) /{\epsilon}), where d is
the dimension of the optimization function. The quantum negative curvature
finding algorithm is exponentially faster than any known classical method which
takes time at least O(d /\sqrt{\epsilon}). Moreover, we propose an efficient
quantum algorithm to achieve the classical read-out of the target state. Our
classical read-out algorithm runs exponentially faster on the degree of d than
existing counterparts.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int