Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Learning Boolean Linear Functions w.r.t. Product Distributions   The problem of learning Boolean linear functions from quantum examples w.r.t.
the uniform distribution can be solved on a quantum computer using the
Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of
noisy quantum training data, as was observed in arXiv:1702.08255v2 [quant-ph].
However, extensions of these learning algorithms beyond the uniform
distribution have not yet been studied. We employ the biased quantum Fourier
transform introduced in arXiv:1802.05690v2 [quant-ph] to develop efficient
quantum algorithms for learning Boolean linear functions on $n$ bits from
quantum examples w.r.t. a biased product distribution. Our first procedure is
applicable to any (except full) bias and requires $\mathcal{O}(\ln (n))$
quantum examples. The number of quantum examples used by our second algorithm
is independent of $n$, but the strategy is applicable only for small bias.
Moreover, we show that the second procedure is stable w.r.t. noisy training
data and w.r.t. faulty quantum gates. This also enables us to solve a version
of the learning problem in which the underlying distribution is not known in
advance. Finally, we prove lower bounds on the classical and quantum sample
complexities of the learning problem. Whereas classically, $\Omega (n)$
examples are necessary independently of the bias, we are able to establish a
quantum sample complexity lower bound of $\Omega (\ln (n))$ only under an
assumption of large bias. Nevertheless, this allows for a discussion of the
performance of our suggested learning algorithms w.r.t. sample complexity. With
our analysis we contribute to a more quantitative understanding of the power
and limitations of quantum training data for learning classical functions.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio