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Open Access Publications from the University of California

Scholarly Works (2 results)

  • Thesis
  • Peer Reviewed
UC Santa Barbara Electronic Theses and Dissertations (2023)

Quantum computers, once their fault-tolerant versions are built, are widely believed to revolutionize the world, bringing an exponential quantum advantage to problems in chemistry, physics and material science. In this thesis, we explore various problems in theoretical condensed matter physics that are in one way or another related to quantum computers. The first part of this thesis is devoted to Majorana zero-energy modes and topological quantum computing. We describe how Majorana modes can be synthesized in superconductor-semiconductor heterostructures, and emphasize vulnerabilities of the topological phase in such heterostructures to external magnetic fields. We further demonstrate how and to what degree the addition of a magnetic insulator or spin-orbit scattering to a heterostructure can help alleviating the negative effects of external magnetic fields. Additionally, we analyze quantum dot-based measurements of Majorana qubits. In particular, we identify the optimal regime for such measurements, and estimate to what degree external noise sources and coupling of the quantum dot to quasiparticle modes in superconductors affect the fidelity of the measurements. The other part of this thesis is devoted to the many-body physics in quantum circuits. We describe a Floquet circuit model in which projective measurements can drive a dynamical spectral phase transition in otherwise purely unitary dynamics of the circuit. Using random-matrix theory, we analytically calculate various properties of this transition, and analyze how the transition can be revealed in the long-time dynamics of the system.

    Cover page: Problems in condensed matter theory motivated by quantum computers
    • Article
    • Peer Reviewed
    UC Irvine Previously Published Works (2015)
    Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
      Cover page: Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
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