Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying such topological features -- connected components, holes, or voids -- and for determining how such features persist as the data is viewed at different scales. This paper provides quantum algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speedup over classical algorithms for topological data analysis.
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While the OP is wrong about being able to "do everything in parallel" via quantum superposition (we have plenty of no-go theorems when it comes to quantum computers being faster simply due to parallelization) some interesting algorithms that are relevant to data science in general have been developed. For example, this[1] one provides an exponential speedup (over known classical algorithms) for calculating persistent homology, a useful method for identifying scale-independent patterns.
[1]: https://arxiv.org/abs/1408.3106
The actual abstract from http://www.nature.com/ncomms/2016/160125/ncomms10138/abs/nco...:
"Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis."
Arxiv version here: http://arxiv.org/abs/1408.3106
This one is good too:
"Quantum algorithms for topological and geometric analysis of big data"
http://arxiv.org/abs/1408.3106
It uses some of this "applied topology", which I only recently found out about.
http://www.math.upenn.edu/~ghrist/notes.html
Fast compilation is important when compilation occurs at runtime, such as query compilers in modern database systems and WebAssembly virtual machines in modern browsers.
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will.