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A Menagerie Of Symmetry Testing Quantum Algorithms, Margarite Lynn Laborde
A Menagerie Of Symmetry Testing Quantum Algorithms, Margarite Lynn Laborde
LSU Doctoral Dissertations
In Chapter 1, we establish the mathematical background used throughout this thesis. We review concepts from group and representation theory. We further establish fundamental concepts from quantum information. This will allow us to then define the different notions of symmetry necessary in the following chapters. In Chapter 2, we investigate Hamiltonian symmetries. We propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. Furthermore, we show that this algorithm is that this algorithm is DQC1-Complete. Finally, we execute one of our symmetry-testing algorithms on existing quantum computers for simple examples. In Chapter 3, we …
Deformed No-Core Shell Model And Symplectic Effective Field Theory, David Kekejian
Deformed No-Core Shell Model And Symplectic Effective Field Theory, David Kekejian
LSU Doctoral Dissertations
Most nuclei are deformed! This simple fact has been established since Bohr and Mot- telson, and successfully demonstrated from first principles by nuclear structure calculations carried out using the ab-initio Symmetry-Adapted No-Core Shell Model (SA-NCSM) us- ing realistic interactions. This simple fact has been the main driver towards understanding the underlying physics; namely, that symplectic symmetry describes deformation and is a dominant symmetry in all nuclei independent of A (nucleon number) and of the realistic interaction used. These two simple observations laid the foundation of this thesis work to explore the applications of symplectic symmetry towards defining a deformed symplectic …