  The dynamics of nonlinear systems qualitatively change depending on their
parameters, which is called bifurcation. A quantum-mechanical nonlinear
oscillator can yield a quantum superposition of two oscillation states, known
as a Schr\"odinger cat state, via quantum adiabatic evolution through its
bifurcation point. Here we propose a quantum computer comprising such quantum
nonlinear oscillators, instead of quantum bits, to solve hard combinatorial
optimization problems. The nonlinear oscillator network finds optimal solutions
via quantum adiabatic evolution, where nonlinear terms are increased slowly, in
contrast to conventional adiabatic quantum computation or quantum annealing,
where quantum fluctuation terms are decreased slowly. As a result of numerical
simulations, it is concluded that quantum superposition and quantum fluctuation
work effectively to find optimal solutions. It is also notable that the present
computer is analogous to neural computers, which are also networks of nonlinear
components. Thus, the present scheme will open new possibilities for quantum
computation, nonlinear science, and artificial intelligence.
