Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantum algorithm for training wide and deep classical neural networks   Given the success of deep learning in classical machine learning, quantum
algorithms for traditional neural network architectures may provide one of the
most promising settings for quantum machine learning. Considering a
fully-connected feedforward neural network, we show that conditions amenable to
classical trainability via gradient descent coincide with those necessary for
efficiently solving quantum linear systems. We propose a quantum algorithm to
approximately train a wide and deep neural network up to $O(1/n)$ error for a
training set of size $n$ by performing sparse matrix inversion in $O(\log n)$
time. To achieve an end-to-end exponential speedup over gradient descent, the
data distribution must permit efficient state preparation and readout. We
numerically demonstrate that the MNIST image dataset satisfies such conditions;
moreover, the quantum algorithm matches the accuracy of the fully-connected
network. Beyond the proven architecture, we provide empirical evidence for
$O(\log n)$ training of a convolutional neural network with pooling.

33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con