One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup.

翻译：量子退火器的核心应用之一是求解伊辛（Ising）问题。然而，合适的伊辛问题需满足两方面条件：一方面要符合硬件的特定限制，另一方面要能代表实际待求解的原始问题。本文从解析角度评估了此类嵌入式伊辛问题的充分条件，并将其转化为线性优化问题。通过设定以最小化最大绝对问题参数为目标的目标函数，解决了退火器的精度问题。基于若干约束的冗余性，我们证明了在标准嵌入设置（即嵌入顶点诱导树结构）下，形式上指数级庞大的优化问题可被简化，最终在多项式时间内求解。这使得在实际场景中能够构造出可证明等价的嵌入式伊辛问题。