"Quasilinearization Approach to Nonlinear Problems in Physics"

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

0130059 Tabakin Past research on predicting spin observables in the photoproduction of mesons led us to an interest in the general dynamics of spin, which is an integral part of the new field of quantum computing. Examination of strong interaction dynamics led us to the subject of nonlinear interactions. Therefore, the focus of our research evolved into two directions; (1) the application and development of a new approach to solving nonlinear equations and (2) the study of the behavior of qubits (typically an atomic or nuclear spin system) and their role in quantum computing and information. A novel quasilinearization method has already been shown, with Prof. Mandelzweig (Hebrew University), to yield rapid convergence for a wide range of nonlinear Physics problems. We plan to combine that method with a wavelet basis approach to examine nonlinear shock-wave and soliton problems. Development of methods for treating nonlinear dynamics has broad applications in many other fields, such as in biology and economics, where effects are enhanced by dependence on higher powers of interaction. Quantum Computing hopes to use quantum spin effects to perform otherwise impossible computational feats. We will focus on developing a computer simulation of a quantum computer. The time evolution of the spin density matrix for a quantum computer will include quantum gates and error corrections, plus the effect of the environment. The goal will be to study the stability of a quantum computer under the influence of loss of quantum coherence and entanglement. This will indicate the feasibility of producing an actual quantum computer. Graduate student researchers will work in both of these activities, which provide excellent and broad training that will lead to opportunities for them in many directions.