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，能够以高概率在常数时间内优化布尔变量上的特定二次函数。这些函数实质上是伊辛模型的哈密顿量，在退火过程中以高概率达到基态能量。它们已被提出作为求解 SAT 问题的一种方法。这类哈密顿量可视为 Max2XOR 问题，即寻找一种赋值方案，使得最多包含两个变量的 XOR 子句得到满足的数量最大化。本文提出了多种构造工具，用于将 SAT 问题归约到 Max2XOR，并展示了如何利用这些工具将 SAT 实例转化为量子退火器的初始配置。