Quantum annealers (QAs) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined over binary variables (qubits), also known as Ising problems. In the last decade, QA systems as implemented by D-Wave have scaled with Moore-like growth. Current architectures provide 2048 sparsely-connected qubits, and continued exponential growth is anticipated, together with increased connectivity.

We explore the feasibility of such architectures for solving SAT and MaxSAT problems as QA systems scale. We develop techniques for effectively encoding SAT –and, with some limitations, MaxSAT– into Ising problems compatible with sparse QA architectures. We provide the theoretical foundations for this mapping, and present encoding techniques that combine offline Satisfiability and Optimization Modulo Theories with on-the-fly placement and routing. Preliminary empirical tests on a current generation 2048-qubit D-Wave system support the feasibility of the approach for certain SAT and MaxSAT problems.

量子退火器（QA）是专用的量子计算机，通过物理地利用量子效应来最小化离散变量的目标函数。当前的QA平台允许优化在二进制变量（qubit）（也称为Ising问题）上定义的二次目标。在过去的十年中，由D-Wave实施的QA系统随着Moore式的增长而扩展。当前的体系结构提供了2048个稀疏连接的量子位，并且随着连接性的提高，预计将继续呈指数增长。

我们探索这种体系结构解决QA系统规模时解决SAT和MaxSAT问题的可行性。我们开发了有效地将SAT（以及在某些限制下为MaxSAT）编码为与稀疏QA体系结构兼容的Ising问题的技术。我们为这种映射提供了理论基础，并提供了将离线可满足性和优化模理论与动态放置和路由相结合的编码技术。对当前一代2048量子比特D-Wave系统进行的初步经验测试证明了该方法针对某些SAT和MaxSAT问题的可行性。