Quantum Annealers are basically quantum computers that with high probability can optimize certain quadratic functions on Boolean variables in constant time. These functions are basically the Hamiltonian of Ising models that reach the ground energy state, with a high probability, after an annealing process. They have been proposed as a way to solve SAT. These Hamiltonians can be seen as Max2XOR problems, i.e. as the problem of finding an assignment that maximizes the number of XOR clauses of at most 2 variables that are satisfied. In this paper, we present several gadgets to reduce SAT to Max2XOR. We show how they can be used to translate SAT instances to initial configurations of a quantum annealer.

翻译：量子退火器本质上是一种量子计算机，能够在常数时间内以高概率优化布尔变量上的特定二次函数。这些函数本质上是伊辛模型的哈密顿量，在退火过程后以高概率达到基态能量。人们曾提出将其用于求解SAT问题。此类哈密顿量可被视为Max2XOR问题，即寻找一个赋值使得最多两个变量的XOR子句满足数量最大化的优化问题。本文提出了若干将SAT归约到Max2XOR的gadget构造方法，并展示了如何利用这些构造将SAT实例转化为量子退火器的初始配置。