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Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics

Wu, Jiaxin
http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Physics.
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.
Tin-Lun Ho (Advisor)
Nandini Trivedi (Committee Member)
Rolando Valdes Aguilar (Committee Member)
Eric Braaten (Committee Member)
155 p.
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

Recommended Citations

Citations

  • Wu, J. (2019). Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199

    APA Style (7th edition)

  • Wu, Jiaxin. Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199.

    MLA Style (8th edition)

  • Wu, Jiaxin. "Topics in Cold Atoms Related to Quantum Information Processing and A Machine Learning Approach to Condensed Matter Physics." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu156320039156199

    Chicago Manual of Style (17th edition)

osu156320039156199
373
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This open access ETD is published by The Ohio State University and OhioLINK.