  A network of driven nonlinear oscillators without dissipation has recently
been proposed for solving combinatorial optimization problems via quantum
adiabatic evolution through its bifurcation point. Here we investigate the
behavior of the quantum bifurcation machine in the presence of dissipation. Our
numerical study suggests that the output probability distribution of the
dissipative quantum bifurcation machine is Boltzmann-like, where the energy in
the Boltzmann distribution corresponds to the cost function of the optimization
problem. We explain the Boltzmann distribution by generalizing the concept of
quantum heating in a single oscillator to the case of multiple coupled
oscillators. The present result also suggests that such driven dissipative
nonlinear oscillator networks can be applied to Boltzmann sampling, which is
used, e.g., for Boltzmann machine learning in the field of artificial
intelligence.
