Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum advantage for differential equation analysis   Quantum algorithms for both differential equation solving and for machine
learning potentially offer an exponential speedup over all known classical
algorithms. However, there also exist obstacles to obtaining this potential
speedup in useful problem instances. The essential obstacle for quantum
differential equation solving is that outputting useful information may require
difficult post-processing, and the essential obstacle for quantum machine
learning is that inputting the training set is a difficult task just by itself.
In this paper, we demonstrate, when combined, these difficulties solve one
another. We show how the output of quantum differential equation solving can
serve as the input for quantum machine learning, allowing dynamical analysis in
terms of principal components, power spectra, and wavelet decompositions. To
illustrate this, we consider continuous time Markov processes on
epidemiological and social networks. These quantum algorithms provide an
exponential advantage over existing classical Monte Carlo methods.

27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con