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The Ohio State University

1. Wu, Jiaxin. Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics.

Degree: PhD, Physics, 2019, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199

This thesis is mainly focused on three topics:
Majorana excitations in a number-conserving model, manipulation of
quasi-particle excitations in quantum Hall systems, and a new
machine learning algorithm to find the ground states of a general
Hamiltonian.In condensed matter physics, Majorana fermions are
emergent excitations which are candidates for quantum memory and
topological quantum computation. The first and simplest model
revealing these excitations does not conserve particle number. Its
experimental realization in solid state materials is difficult and
still under debate. In comparison, cold atoms provide an
alternative platform to realize these exotic excitations. However,
cold atoms experiments require the system to be number-conserving.
Theoretically, it is not yet clear whether there is a model
realizable in cold atoms that also hosts these exotic excitations.
In this thesis, we investigate such a number-conserving model and
show that it has the same phase diagram and very similar
excitations. Although the ground state degeneracy, as one of the
signature properties of the original Majorana model crucial for
quantum memory, is not present when the total particle number is
fixed, one can recover the degeneracy by allowing tunnelling to
change the total particle number.As for the quantum Hall system, we
discuss how to control quasi-hole excitations with sharp external
potentials where the system has integer filling factor. The eigen
wavefunctions of the quasiholes are discussed in details. Our
motivation is that most discussions or experiments regarding
quantum Hall systems mainly focus on transport properties, but
topological quantum computation may require one to have more
precise control over the quasiparticle excitations. Although the
ultimate goal is to control the non-Abelian excitations predicted
in fractional quantum Hall systems, our results, especially in the
situation with contact interactions, pave a way to explore this
problem analytically. We also demonstrate some basic ideas of
manipulating the quantum states, including non-Abelian exchange, in
the integer quantum Hall systems. The last topic is about a new
machine learning algorithm to find the unbiased ground states of a
general Hamiltonian. Solving ground states of quantum many-body
systems has been a long-standing problem in condensed matter
physics, since the Hilbert space grows exponentially with the
system size. In this thesis, we attempt to address this problem
with a new unsupervised machine learning algorithm utilizing the
benefits of artificial neural network. Without assuming the
specific forms of the eigenvectors, our algorithm can find the
eigenvectors in an unbiased way with well controlled accuracy. As
examples, we apply this algorithm to 1D Ising and Heisenberg
models, where the results match very well with exact
diagonalization. Furthermore, we point out how this method can
potentially be applied to large systems beyond exact
diagonalization.
*Advisors/Committee Members: Ho, Tin-Lun (Advisor).*

Subjects/Keywords: Physics; quantum information processing; cold atoms; number-conserving; Majorana; quantum Hall; quasiparticle wavefunction; singlet; non-Abelian exchange; machine learning; ground states; quantum many-body systems; artificial neural network

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APA (6^{th} Edition):

Wu, J. (2019). Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199

Chicago Manual of Style (16^{th} Edition):

Wu, Jiaxin. “Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics.” 2019. Doctoral Dissertation, The Ohio State University. Accessed November 17, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199.

MLA Handbook (7^{th} Edition):

Wu, Jiaxin. “Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics.” 2019. Web. 17 Nov 2019.

Vancouver:

Wu J. Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics. [Internet] [Doctoral dissertation]. The Ohio State University; 2019. [cited 2019 Nov 17]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199.

Council of Science Editors:

Wu J. Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics. [Doctoral Dissertation]. The Ohio State University; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199