Incorporating external fields in analog Ising machines

Ising machines are specialized devices designed to efficiently solve combinatorial optimization problems. They consist of artificial spins that evolve towards a low-energy configuration representing a problem’s solution. Most realistic problems require both spin-spin couplings and external fields. In Ising machines with analog spins, these interactions scale differently with the continuous spin amplitudes, leading to imbalances that affect performance. Various techniques have been proposed to mitigate this issue, but their performance has not been benchmarked. We address this gap through a numerical analysis. We evaluate the time-to-solution of these methods across three distinct problem classes with up to 2400 spins. Our results show that the most effective way to incorporate external fields is through an approach where the spin interactions are proportional to the spin signs, rather than their continuous amplitudes. Solving real-world optimization problems on analog Ising machines requires the use of external fields that bias individual spins. This work shows that the best performance is achieved using spin interactions proportional to the spin signs rather than their analog amplitudes.