Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum query complexity of symmetric oracle problems   We study the query complexity of quantum learning problems in which the
oracles form a group $G$ of unitary matrices. In the simplest case, one wishes
to identify the oracle, and we find a description of the optimal success
probability of a $t$-query quantum algorithm in terms of group characters. As
an application, we show that $\Omega(n)$ queries are required to identify a
random permutation in $S_n$. More generally, suppose $H$ is a fixed subgroup of
the group $G$ of oracles, and given access to an oracle sampled uniformly from
$G$, we want to learn which coset of $H$ the oracle belongs to. We call this
problem coset identification and it generalizes a number of well-known quantum
algorithms including the Bernstein-Vazirani problem, the van Dam problem and
finite field polynomial interpolation. We provide character-theoretic formulas
for the optimal success probability achieved by a $t$-query algorithm for this
problem. One application involves the Heisenberg group and provides a family of
problems depending on $n$ which require $n+1$ queries classically and only $1$
query quantumly.

15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int