  The coherent Ising machine (CIM) enables efficient sampling of low-lying
energy states of the Ising Hamiltonian with all-to-all connectivity by encoding
the spins in the amplitudes of pulsed modes in an optical parametric oscillator
(OPO). The interaction between the pulses is realized by means of
measurement-based optoelectronic feedforward which enhances the gain for
lower-energy spin configurations. We present an efficient method of simulating
the CIM on a classical computer that outperforms the CIM itself as well as the
noisy mean-field annealer in terms of both the quality of the samples and the
computational speed. It is furthermore advantageous with respect to the CIM in
that it can handle Ising Hamiltonians with arbitrary real-valued node coupling
strengths. These results illuminate the nature of the faster performance
exhibited by the CIM and may give rise to a new class of quantum-inspired
algorithms of classical annealing that can successfully compete with existing
methods.
