서브메뉴
검색
Quantum Computing and Machine Learning Approaches to Quantum Many-Body Physics
Quantum Computing and Machine Learning Approaches to Quantum Many-Body Physics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151126
- ISBN
- 9798383182659
- DDC
- 530
- 저자명
- Sheng, Shiyi.
- 서명/저자
- Quantum Computing and Machine Learning Approaches to Quantum Many-Body Physics
- 발행사항
- [Sl] : University of Maryland, College Park, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 174 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
- 주기사항
- Advisor: Bedaque, Paulo F.
- 학위논문주기
- Thesis (Ph.D.)--University of Maryland, College Park, 2024.
- 초록/해제
- 요약Lattice field theory provides a framework for which to explore properties of quantum field theories non-perturbatively. However for certain lattice calculations, for example when considering real-time dynamics or fermionic systems at finite density, sign problems occur which render those calculations intractable. One approach to solving the sign problem is to avoid it altogether by instead considering a simulation of the field theory on a quantum computer. For bosonic field theories, a procedure of qubitizing the bosonic fields is a necessary first step. The infinite-dimensional Hilbert space of the bosonic fields must be properly truncated as to encode those fields on a finite-dimensional Hilbert space spanned by the qubits on the quantum computer.This thesis first discusses various strategies of making such a truncation. Ideally, the truncation yields a discrete spin system that contains a critical point in the same universality class as the untruncated field theory. That way, the physics of the original field theory is reproduced in the continuum limit of the truncated theory without needing to take a second limit of removing the truncation. Simulations of different models arising from various truncation strategies of the (1+1)-dimensional O(3) nonlinear sigma model are performed and different qubitizations for SU(2) gauge fields are considered and proposed. Due to a lack of an efficient method for solving many-body systems in more than one dimension, numerical simulations of these SU(2) qubitizations are unavailable.The second half of the thesis explores the use of machine learning techniques in providing effective ways to solve quantum many-body problems. Neural network structures, such as feed-forward networks and restricted Boltzmann machines are universal approximators for continuous and discrete functions respectively. Therefore, they can be used as flexible wave function ansatze. Gradient descent algorithms can be applied to variationally search the general functional space spanned by neural-network-based ansatze for ground states of interacting, many-body systems. An ansatz is constructed explicitly for a system of indistinguishable bosons in one dimension and tested by comparing numerical results with analytic solutions of several exactly-solvable models. An extension of these neural-network ansatze to systems of identical bosons and fermions and discrete spin systems in higher dimensions would allow for concrete simulations of systems ranging from nuclei and qubitization models.
- 일반주제명
- Physics
- 일반주제명
- Quantum physics
- 일반주제명
- Computational physics
- 일반주제명
- Theoretical physics
- 키워드
- Machine learning
- 기타저자
- University of Maryland, College Park Physics
- 기본자료저록
- Dissertations Abstracts International. 86-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017160852
■00520250211151126
■006m o d
■007cr#unu||||||||
■020 ▼a9798383182659
■035 ▼a(MiAaPQ)AAI31147077
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aSheng, Shiyi.▼0(orcid)0000-0002-6168-8131
■24510▼aQuantum Computing and Machine Learning Approaches to Quantum Many-Body Physics
■260 ▼a[Sl]▼bUniversity of Maryland, College Park▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a174 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-01, Section: B.
■500 ▼aAdvisor: Bedaque, Paulo F.
■5021 ▼aThesis (Ph.D.)--University of Maryland, College Park, 2024.
■520 ▼aLattice field theory provides a framework for which to explore properties of quantum field theories non-perturbatively. However for certain lattice calculations, for example when considering real-time dynamics or fermionic systems at finite density, sign problems occur which render those calculations intractable. One approach to solving the sign problem is to avoid it altogether by instead considering a simulation of the field theory on a quantum computer. For bosonic field theories, a procedure of qubitizing the bosonic fields is a necessary first step. The infinite-dimensional Hilbert space of the bosonic fields must be properly truncated as to encode those fields on a finite-dimensional Hilbert space spanned by the qubits on the quantum computer.This thesis first discusses various strategies of making such a truncation. Ideally, the truncation yields a discrete spin system that contains a critical point in the same universality class as the untruncated field theory. That way, the physics of the original field theory is reproduced in the continuum limit of the truncated theory without needing to take a second limit of removing the truncation. Simulations of different models arising from various truncation strategies of the (1+1)-dimensional O(3) nonlinear sigma model are performed and different qubitizations for SU(2) gauge fields are considered and proposed. Due to a lack of an efficient method for solving many-body systems in more than one dimension, numerical simulations of these SU(2) qubitizations are unavailable.The second half of the thesis explores the use of machine learning techniques in providing effective ways to solve quantum many-body problems. Neural network structures, such as feed-forward networks and restricted Boltzmann machines are universal approximators for continuous and discrete functions respectively. Therefore, they can be used as flexible wave function ansatze. Gradient descent algorithms can be applied to variationally search the general functional space spanned by neural-network-based ansatze for ground states of interacting, many-body systems. An ansatz is constructed explicitly for a system of indistinguishable bosons in one dimension and tested by comparing numerical results with analytic solutions of several exactly-solvable models. An extension of these neural-network ansatze to systems of identical bosons and fermions and discrete spin systems in higher dimensions would allow for concrete simulations of systems ranging from nuclei and qubitization models.
■590 ▼aSchool code: 0117.
■650 4▼aPhysics
■650 4▼aQuantum physics
■650 4▼aComputational physics
■650 4▼aTheoretical physics
■653 ▼aMachine learning
■653 ▼aQuantum computing
■653 ▼aLattice field theory
■653 ▼aQuantum field theories
■653 ▼aMany-body physics
■690 ▼a0605
■690 ▼a0599
■690 ▼a0216
■690 ▼a0753
■71020▼aUniversity of Maryland, College Park▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-01B.
■790 ▼a0117
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160852▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
