The dynamics of nonlinear systems qualitatively change depending on theirparameters, which is called bifurcation. A quantum-mechanical nonlinearoscillator can yield a quantum superposition of two oscillation states, knownas a Schr\"odinger cat state, via quantum adiabatic evolution through itsbifurcation point. Here we propose a quantum computer comprising such quantumnonlinear oscillators, instead of quantum bits, to solve hard combinatorialoptimization problems. The nonlinear oscillator network finds optimal solutionsvia quantum adiabatic evolution, where nonlinear terms are increased slowly, incontrast to conventional adiabatic quantum computation or quantum annealing,where quantum fluctuation terms are decreased slowly. As a result of numericalsimulations, it is concluded that quantum superposition and quantum fluctuationwork effectively to find optimal solutions. It is also notable that the presentcomputer is analogous to neural computers, which are also networks of nonlinearcomponents. Thus, the present scheme will open new possibilities for quantumcomputation, nonlinear science, and artificial intelligence.
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