40,418 research outputs found
Quantum image classification using principal component analysis
We present a novel quantum algorithm for classification of images. The
algorithm is constructed using principal component analysis and von Neuman
quantum measurements. In order to apply the algorithm we present a new quantum
representation of grayscale images.Comment: 9 page
Quantum Eigenfaces: Linear Feature Mapping and Nearest Neighbor Classification with Outlier Detection
We propose a quantum machine learning algorithm for data classification, inspired by the seminal computer vision approach of eigenfaces for face recognition. The algorithm enhances nearest neighbor/centroid classifiers with concepts from principal component analysis, enabling the automatic detection of outliers and finding use in anomaly detection domains beyond face recognition. Assuming classical input data, we formalize how to implement the algorithm using a quantum random access memory and state-of-the-art quantum linear algebra, discussing the complexity of performing the classification algorithm on a fault-tolerant quantum device. The asymptotic time complexity analysis shows that the quantum classification algorithm can be more efficient than its classical counterpart. We showcase an application of this algorithm for face recognition and image classification datasets with anomalies, obtaining promising results for the running time parameters. This work contributes to the growing field of quantum machine learning applications, and the algorithm's simplicity makes it easily adoptable by future quantum machine learning practitioners
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
The Structure of Line Bundles over Quantum Teardrops
Over the quantum weighted 1-dimensional complex projective spaces, called
quantum teardrops, the quantum line bundles associated with the quantum
principal U(1)-bundles introduced and studied by Brzezinski and Fairfax are
explicitly identified among the finitely generated projective modules which are
classified up to isomorphism. The quantum lens space in which these quantum
line bundles are embedded is realized as a concrete groupoid C*-algebra
Laser Based Mid-Infrared Spectroscopic Imaging – Exploring a Novel Method for Application in Cancer Diagnosis
A number of biomedical studies have shown that mid-infrared spectroscopic images can provide
both morphological and biochemical information that can be used for the diagnosis of cancer. Whilst
this technique has shown great potential it has yet to be employed by the medical profession. By
replacing the conventional broadband thermal source employed in modern FTIR spectrometers with
high-brightness, broadly tuneable laser based sources (QCLs and OPGs) we aim to solve one of the
main obstacles to the transfer of this technology to the medical arena; namely poor signal to noise
ratios at high spatial resolutions and short image acquisition times. In this thesis we take the first
steps towards developing the optimum experimental configuration, the data processing algorithms
and the spectroscopic image contrast and enhancement methods needed to utilise these high
intensity laser based sources. We show that a QCL system is better suited to providing numerical
absorbance values (biochemical information) than an OPG system primarily due to the QCL pulse
stability. We also discuss practical protocols for the application of spectroscopic imaging to cancer
diagnosis and present our spectroscopic imaging results from our laser based spectroscopic imaging
experiments of oesophageal cancer tissue
Reflection positivity and invertible topological phases
We implement an extended version of reflection positivity (Wick-rotated
unitarity) for invertible topological quantum field theories and compute the
abelian group of deformation classes using stable homotopy theory. We apply
these field theory considerations to lattice systems, assuming the existence
and validity of low energy effective field theory approximations, and thereby
produce a general formula for the group of Symmetry Protected Topological (SPT)
phases in terms of Thom's bordism spectra; the only input is the dimension and
symmetry group. We provide computations for fermionic systems in physically
relevant dimensions. Other topics include symmetry in quantum field theories, a
relativistic 10-fold way, the homotopy theory of relativistic free fermions,
and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3
major revision; v4 minor revision: corrected proof of Lemma 9.55, many small
changes throughout; v5 version for publication in Geometry & Topolog
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