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A Qubit Algorithm for Simulating the Nonlinear Schroedinger Equation

Simpson, Connor
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.
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2019-05-01
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Undergraduate Honors Theses
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Vahala, George
Aubin, Seth
Vahala, George
Haug, Matthew
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Physics
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https://scholarworks.wm.edu/handle/internal/10781
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