Machine Learning approaches to Quantum Materials: Quantifying Entanglement

1 Motivation and problem statement
Machine Learning methods are now widely used in many areas of science, usually as a tool to deal
with large amount of data [1][2]. However, it was shown recently that Artificial Intelligence can also
be used in the field of condensed matter physics to detect the phase transitions of some fundamental
models [3] or establish the entanglement transitions from magnetic neutron scattering experiment
[4], which suggest that these methods may serve as an alternative to standard analysis of physical
systems. The main goal of this PhD thesis is to invent a method of quantifying the entanglement
of many-body systems using neural networks approach. This is motivated by the fact that current
techniques to measure the entanglement can not be applied to general systems and usually are only
evaluated in theoretical work, where the Machine Learning approach could in principle be applied
to measurements from experiment. The other original work that is planned for this PhD thesis is to
obtain the density matrix of systems using artificial neural networks, which allows for studying the
materials at finite temperatures.
2 Significance of research
The method of experimental measurement of entanglement would be of much interest, especially in
emerging field of quantum computing. Ideally the technique invented in this thesis could be applied
in a similar fashion as the other well established methods of data analysis e.g. fitting the function
obtained from theoretical model. One of additional features would be that the neural networks can
be set to analyse the data in unbiased way, which allows for studying systems which do not have a
theoretical description.
3 Planned work
Learning about the Machine Learning techniques and their current application in physics by
analysing the data from muon Spin Rotation experiment using Principal Component Analysis.
Applying the neural networks to obtain the descriptions (partition function, density matrix) of
few chosen many-body systems at finite temperatures.
Calculating the entanglement using existing methods and simultaneously obtaining observables,
which are then introduced to neural networks to check for the correlations between entanglement
and observables.
Applying the established method to experimental data.