Efficient Coefficient Bit-Width Reduction Method for Ising Machines

Ising machines such as quantum annealing machines and semiconductor-based annealing machines can solve various combinatorial optimization problems very efficiently by transforming it into a data structure called an Ising model. At that time, the bit-widths of the coefficients of the Ising model have to be kept within the range that an Ising machine can deal with. However, by reducing the Ising-model bit-widths, its minimum energy state, or ground state, may become different from that of the original one and hence the targeted combinatorial optimization problem cannot be well solved. This paper proposes an effective method for reducing Ising-model bit-widths. The proposed method is composed of the two processes: First, given an Ising model with large coefficient bit-widths, the shift method is applied to reduce its bit-widths roughly. Second, the spin-adding method is applied to further reduce its bit-widths to those that Ising machines can deal with. Without adding too many extra spins, we efficiently reduce the coefficient bit-widths of the original Ising model. Furthermore, the ground state before and after reducing the coefficient bit-widths is not much changed in most of the practical cases. Experimental evaluations demonstrate the effectiveness of the proposed method, compared to existing methods.