  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.
