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arXiv:quant-ph/0307116

Nonlinear Schrodinger Equation for Quantum Computation

M. Cemal Yalabık

Published Jul 17, 2003• 0 citations
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Abstract

Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of problems. An example of such a system for implementing the logical NOR operation is demonstrated.
DOI
10.48550/arxiv.quant-ph/0307116

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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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