Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Lower Bounds for Tripartite Versions of the Hidden Shift and the
  Set Equality Problems   In this paper, we study quantum query complexity of the following rather
natural tripartite generalisations (in the spirit of the 3-sum problem) of the
hidden shift and the set equality problems, which we call the 3-shift-sum and
the 3-matching-sum problems.
  The 3-shift-sum problem is as follows: given a table of $3\times n$ elements,
is it possible to circularly shift its rows so that the sum of the elements in
each column becomes zero? It is promised that, if this is not the case, then no
3 elements in the table sum up to zero. The 3-matching-sum problem is defined
similarly, but it is allowed to arbitrarily permute elements within each row.
For these problems, we prove lower bounds of $\Omega(n^{1/3})$ and
$\Omega(\sqrt n)$, respectively. The second lower bound is tight.
  The lower bounds are proven by a novel application of the dual learning graph
framework and by using representation-theoretic tools.

31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin