Date Thesis Awarded
5-2019
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Physics
Advisor
George Vahala
Committee Members
Seth Aubin
George Vahala
Matthew Haug
Abstract
Recent work in mathematical physics and nonlinear optics has shown that Hamiltonians that are non-Hermitian but still symmetric under parity and time reversal can describe eigenstates of a system with real eigenvalues. Other research has also showed that the nonlinear Schrodinger equation can be generalized to describe PT-symmetric systems, which generates novel solutions not described by its Hermitian equivalent. The Hermitian form of the nonlinear Schroedinger equation can also be extended to describe a particular case of the general PT-symmetric NLS, suggesting a connection between the two. I attempted to generate a unitary operator that will be useful for unitary quantum algorithms describing a coupled set of nonlinear Schroedinger equations and the PT-symmetric version of the NLS.
Recommended Citation
Simpson, Connor, "A Qubit Algorithm for Simulating the Nonlinear Schroedinger Equation" (2019). Undergraduate Honors Theses. William & Mary. Paper 1382.
https://scholarworks.wm.edu/honorstheses/1382
