An optical Ising machine based on multi-core fiber lasers

Many important problems such as the Graph Partition Problem (GPP) and MAX-CUT problems can be formulated as searching problems of a ground state of an Ising system. Therefore, developing an Ising machine that can find efficiently the ground state of Ising system has been attracted great efforts and activities in recent years. An Ising machine that utilizes the effects of Bose-Einstein condensation and measurement-feedback control has been proposed [1]. However quantum coherence between the different Ising sites is difficult to achieve due to the measurement feedback circuit. An Ising machine that based on a system of coupled slave lasers that are driven coherently by a master laser has been proposed [2]. The modeling results for the VCSEL-based system show Ising states in the system can be reached in about a nanosecond. However, the results also show low output power (small number of photons ∼10⁴-10⁵) and the complex system that control couplings between master and slave lasers and among slave lasers could be very challenging to realize experimentally. Recently, an Ising machine based on a system of 4 coherently coupled optical parametric oscillators (OPO) has been demonstrated experimentally for the first time [3]. That achievement although is a significant breakthrough in the field, but it can only describe a limit case of Ising Hamiltonian without Zeeman term. Furthermore, the way of generation of cross couplings among the Ising spins (OPOs) would only provide positive coupling coefficients thus prevent it from describing general applications which can have both negative and positive values of the coefficients.