This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable optimization. The former is an improvement on the existing algorithm in a special case. The latter is realized by means of the maximal independent point set in graph theory. We apply this new method in integer factorization on quantum annealers and achieve the largest integer factorization (4137131) with 93 variables, the range of coefficients is [-1024,1024] which is much smaller than the previous results. We also focus on the quantum attacks on block ciphers and present an efficient method with smaller coefficients to transform Boolean equation systems into QUBO problems.

翻译：本文为QUBO问题提供了一个将假 Boolean 函数优化到QUBO 问题的新方法,可以通过量子射线器加以解决。 新方法有两个方面, 一个是系数优化, 另一个是变量优化。 前者是特殊情况中现有算法的改进。 后者是通过图形理论中最大独立点设定的实现的。 我们用这一新的方法对量子射线器进行整数系数化( 4137131), 并用93个变量实现最大整数系数化( 4137131), 系数范围[ 1024, 大大小于先前的结果。 我们还侧重于对区密码的量攻击, 并提出一种将布林方程式系统转化为QUBO问题的高效方法, 其系数较小。