An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable groups. The main idea of a promising approach to the shift problem is reduction to solving systems of certain random disequations in finite abelian groups. The random disequations are actually generalizations of linear functions distributed nearly uniformly over those not containing a specific group element in the kernel. In this paper we give an algorithm which finds the solutions of a system of N random linear disequations in an abelian p-group A in time polynomial in N, where N=(log|A|)^{O(q)}, and q is the exponent of A.

隐子群问题的一个重要子例等价于 交换群上的移位问题。后一个问题的有效解决方案 将作为量子隐子群算法的构建块 可解群。解决换挡问题的一种有前景的方法的主要思想是 有限阿贝尔空间中某些随机方程组解的化简 组。随机方程实际上是线性方程的推广 函数几乎均匀地分布在不包含特定 内核中的组元素。在这篇文章中，我们给出了一个算法，它可以找到 交换P-群A中N个随机线性方程组的解 在N中的时间多项式，其中N=(log|A|)^{O(Q)}，Q是A的指数。