The coherent Ising machine (CIM) is designed to solve the NP-hard Ising problem quickly and energy efficiently. Boolean satisfiability (SAT) and maximum satisfiability (Max-SAT) are classes of NP-complete and NP-hard problems that are equally important and more practically relevant combinatorial optimization problems. Many approaches exist for solving Boolean SAT, such as quantum annealing and classical stochastic local search (SLS) solvers; however, they all are expected to require many steps to solve hard SAT problems and, thus, require large amounts of time and energy. In addition, a SAT problem can be converted into an Ising problem and solved by an Ising machine; however, we have found that this approach has drawbacks. As well as reviewing existing approaches to solving the SAT problem, we have extended the CIM algorithm and architecture to solve SAT and Max-SAT problems directly. This new technique is termed a coherent SAT solver (CSS). We have studied three implementations of the CSS, all-optical, hybrid optical–digital and all digital (cyber-CSS), and have compared the time-to-solution and energy-to-solution of three machines. The cyber-CSS, which is already implemented using a graphics processing unit (GPU), demonstrates competitive performance against existing SLS solvers such as probSAT. The CSS is also compared with another continuous-time SAT solver known as the CTDS, and the scaling behavior is evaluated for random 3-SAT problems. The hybrid optical–digital CSS is a more performant and practical machine that can be realized in a short term. Finally, the all-optical CSS promises the best energy-to-solution cost; however various technical challenges in nonlinear optics await us in order to build this machine.

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Coherent SAT 求解器：教程

相干伊辛机（CIM）旨在快速、高效地解决 NP 难伊辛问题。布尔可满足性 (SAT) 和最大可满足性 (Max-SAT) 是 NP 完全问题和 NP 困难问题的类别，它们同样重要且更实际相关的组合优化问题。解决布尔 SAT 问题的方法有很多，例如量子退火和经典随机局部搜索 (SLS) 求解器；然而，它们都需要采取许多步骤来解决 SAT 难题，因此需要大量的时间和精力。另外，SAT问题可以转化为Ising问题，通过Ising机来求解；然而，我们发现这种方法有缺陷。除了回顾解决 SAT 问题的现有方法外，我们扩展了 CIM 算法和架构来直接解决 SAT 和 Max-SAT 问题。这种新技术被称为相干 SAT 求解器 (CSS)。我们研究了CSS的三种实现方式，即全光学、混合光学数字和全数字（网络CSS），并比较了三台机器的解决时间和解决能量。cyber-CSS 已使用图形处理单元 (GPU) 实现，与 probSAT 等现有 SLS 求解器相比，其性能具有竞争力。CSS 还与另一个称为 CTDS 的连续时间 SAT 求解器进行了比较，并针对随机 3-SAT 问题评估了缩放行为。混合光学数字 CSS 是一种性能更高、更实用的机器，可以在短期内实现。最后，全光 CSS 保证了最佳的能源解决方案成本；然而，为了建造这台机器，非线性光学领域的各种技术挑战等待着我们。