多项式时间内嵌入式Ising问题的最优充分条件
Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time
AI总结：
针对量子退火器求解Ising问题的硬件约束与精度问题，研究解析嵌入式Ising问题的充分条件并转化为线性优化问题，证明标准树嵌入场景下可多项式时间求解，实现可证等价的实际问题构建。
摘要：
量子退火器的核心应用之一是求解Ising问题的解。然而，合适的Ising问题需要被构建为一方面满足硬件的特定限制，另一方面代表实际需要求解的原始问题。我们通过解析方式评估了此类嵌入式Ising问题的充分条件，并将其转化为一个线性优化问题。通过以最小化最大绝对问题参数为目标函数，解决了退火器的精度问题。由于若干约束存在冗余，我们可以证明，在嵌入式顶点构成树的标准嵌入场景下，形式上呈指数规模的优化问题可以被约简，最终在多项式时间内求解。这使得在实际场景中构建可证明等价的嵌入式Ising问题成为可能。
英文摘要：
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.
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