Report: Exploring Machine Learning's Role in Quantum Physics

This report explores the application of machine learning in quantum physics, highlighting its potential to revolutionize the field. It begins by introducing machine learning as a core element of artificial intelligence, emphasizing its use in making predictions and decisions. The report then addresses the 'curse of dimensionality' problem in machine learning, particularly in the context of quantum systems. It details the use of machine learning in uncovering phases of matter and other areas of physics, with a focus on algorithms and models like the restricted Boltzmann machine (RBM) and neural networks. The report explains how these models are used to represent quantum states, solve quantum many-body problems, and address the phenomenon of entanglement. The application of these techniques in quantum state tomography is also discussed, providing a comprehensive overview of how machine learning is transforming the study of quantum physics.

PHYSICS
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Machine learning is a disciple in computer studies that deals with
developing computers that are able to make a prediction about some things
like weather forecasting and also make a decision in some cases like
driverless cars, gaming and also Google translators.
Thus machine learning is the core of artificial intelligence.

In order to make the machine learn and perform better it needs to be
trained and tweaked.
 Machine learning has a bigger problem which is known as curse
dimensionality.
This affects the machine learning in a case where the dimensional space
becomes bigger, it will be difficult to manage the machine learning
(Trachanas, 2018)

This problem of machine learning is due to a quantum machine in a case
where exponential data are needed to describe the quantum state of many
bodies.
 Machine learning is also employed in other disciplines of physics like in
studying of galaxies and stars, it is also employed in learning of electrons.
The use of machine learning may seem to be science fiction but the reality is
that machine learning and its application have progressed over several
decades.

Uncovering phases of matter
While applying machine learning a clear strategy is employed where
the algorithms of machine learning are properly trained.
For example, when a machine is trained to identify a face of a dog and
a cat, there will be several images of a cat and a dog which will enable
the machine to learn perfectly the right image of a dog and the right
image of a cat.

Instead of using cats and dogs, a Monte Carlo simulation model of
restricted-boltzmann-machine representation.
Figure 1: Showing restricted-boltzmann-machine
representation

TWO REPRESENTATIONS
 In this case the representation of machine learning is given for the
visible layer and the hidden layer which is a Boltzmann representation of
neural network (Sankar Das Sarma, 2019).
And for model representation, the visible layer is donated by N while the
hidden layer is denoted by M.

The visible layer is always linked to the hidden layer and neurons which are in
the same layer cannot be connected. This is illustrated in the following
diagram;
Figure 2: Showing a representation of two-layer model

Neural-network representation
 Machine learning algorithms are better expressed in a model of artificial
neural networks in solving quantum state problems.
In solving this exponential amount information is used where for example N
quantum bits having 2 possible configurations of either 1s or 0s hence the
total possible configuration will be 2N.

Entanglement in neural-network states
This is a state where the measurement of one particle will greatly
manipulate the state of another even if the particle is isolated by a larger
distance.
This phenomenon is for the case of Bekenstein Hawking entropy for a
black hole. This can be illustrated using the following diagram;
Figure 3: Showing a neural network

Quantum many-body problems
In obtaining the problem of quantum for many bodies, we can find either
the dynamic of the system or the ground state of the system.
And this can be realized through the use of RBM model. The technique
of RBM has been employed in quantum state tomography.

Reference
Sankar Das Sarma, D.-L. (2019). MACHINE LEARNING meets quantum
physics . Beijing: Springer press.
Trachanas, S. (2018). An Introduction to Quantum Physics: A First Course
for Physicists, Chemists, Materials Scientists, and Engineers. Liverpool:
John Wiley & Sons.