47 research outputs found
Nonnegative/binary matrix factorization with a D-Wave quantum annealer
D-Wave quantum annealers represent a novel computational architecture and
have attracted significant interest, but have been used for few real-world
computations. Machine learning has been identified as an area where quantum
annealing may be useful. Here, we show that the D-Wave 2X can be effectively
used as part of an unsupervised machine learning method. This method can be
used to analyze large datasets. The D-Wave only limits the number of features
that can be extracted from the dataset. We apply this method to learn the
features from a set of facial images
Classification Problem in a Quantum Framework
The aim of this paper is to provide a quantum counterpart of the well known
minimum-distance classifier named Nearest Mean Classifier (NMC). In particular,
we refer to the following previous works: i) in Sergioli et al. 2016, we have
introduced a detailed quantum version of the NMC, named Quantum Nearest Mean
Classifier (QNMC), for two-dimensional problems and we have proposed a
generalization to abitrary dimensions; ii) in Sergioli et al. 2017, the
n-dimensional problem was analyzed in detail and a particular encoding for
arbitrary n-feature vectors into density operators has been presented. In this
paper, we introduce a new promizing encoding of arbitrary n-dimensional
patterns into density operators, starting from the two-feature encoding
provided in the first work. Further, unlike the NMC, the QNMC shows to be not
invariant by rescaling the features of each pattern. This property allows us to
introduce a free parameter whose variation provides, in some case, an
improvement of the QNMC performance. We show experimental results where: i) the
NMC and QNMC performances are compared on different datasets; ii) the effects
of the non-invariance under uniform rescaling for the QNMC are investigated.Comment: 11 pages, 2 figure
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of
machine learning using quantum computers. We describe the main results known
for three models of learning: exact learning from membership queries, and
Probably Approximately Correct (PAC) and agnostic learning from classical or
quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation.
This version will appear as Complexity Theory Column in SIGACT News in June
2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a
referenc