%20problems%20to%20apply%20an%20Ising%20machine.%20However%2C%20current%20state-of-the-art%20Ising%20machines%20still%20often%20fail%20to%20output%20near-optimal%20solutions%20due%20to%20the%20complicated%20energy%20landscape%20of%20QUBO%20problems.%20Furthermore%2C%20the%20physical%20implementation%20of%20Ising%20machines%20severely%20restricts%20the%20size%20of%20QUBO%20problems%20to%20be%20input%20as%20a%20result%20of%20limited%20hardware%20graph%20structures.%20In%20this%20study%2C%20we%20take%20a%20new%20approach%20to%20these%20challenges%20by%20injecting%20auxiliary%20penalties%20preserving%20the%20optimum%2C%20which%20reduces%20quadratic%20terms%20in%20QUBO%20objective%20functions.%20The%20process%20simultaneously%20simplifies%20the%20energy%20landscape%20of%20QUBO%20problems%2C%20allowing%20the%20search%20for%20near-optimal%20solutions%2C%20and%20makes%20QUBO%20problems%20sparser%2C%20facilitating%20encoding%20into%20Ising%20machines%20with%20restriction%20on%20the%20hardware%20graph%20structure.%20We%20propose%20linearization%20of%20QUBO%20problems%20using%20variable%20posets%20as%20an%20outcome%20of%20the%20approach.%20By%20applying%20the%20proposed%20method%20to%20synthetic%20QUBO%20instances%20and%20to%20multi-dimensional%20knapsack%20problems%2C%20we%20empirically%20validate%20the%20effects%20on%20enhancing%20minor-embedding%20of%20QUBO%20problems%20and%20the%20performance%20of%20Ising%20machines.)
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