Dmitrii Dobrynin, Adrien Renaudineau, Mohammad Hizzani, Dmitri Strukov, Masoud Mohseni, John Paul Strachan
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引用次数: 0
摘要
基于物理的伊辛机(Ising machine,IM)以更高的速度和更好的能效迎接了解决硬组合优化问题的挑战。一般来说,这类专用系统采用局部搜索启发式方法遍历能量景观来寻找最优解。通过扩展地景几何可视化工具--断开图,我们量化并解决了组合优化领域中 IM 所面临的一些主要挑战。利用高效的采样方法,我们直观地捕捉到了具有不同结构和硬度的问题的景观,这些问题具有很强的退行性,成为 IM 的熵障。此外,我们还研究了将组合问题嵌入伊辛硬件时,由局部性降低方法引起的能量障碍、局部最小值和配置空间集群效应。为此,我们采样了 PUBO 能量图及其不同 QUBO 映射的断开图,并考虑了局部最小值和鞍区。我们证明了 QUBO 能量景观特性导致二次 IM 性能不佳,并提出了改进方向。
Disconnectivity graphs for visualizing combinatorial optimization problems: challenges of embedding to Ising machines
Physics-based Ising machines (IM) have risen to the challenge of solving hard
combinatorial optimization problems with higher speed and better energy
efficiency. Generally, such dedicated systems employ local search heuristics to
traverse energy landscapes in searching for optimal solutions. Extending
landscape geometry visualization tools, disconnectivity graphs, we quantify and
address some of the major challenges met by IMs in the field of combinatorial
optimization. Using efficient sampling methods, we visually capture landscapes
of problems having diverse structure and hardness and featuring strong
degeneracies, which act as entropic barriers for IMs. Furthermore, we
investigate energy barriers, local minima, and configuration space clustering
effects caused by locality reduction methods when embedding combinatorial
problems to the Ising hardware. For this purpose, we sample disconnectivity
graphs of PUBO energy landscapes and their different QUBO mappings accounting
for both local minima and saddle regions. We demonstrate that QUBO energy
landscape properties lead to the subpar performance of quadratic IMs and
suggest directions for their improvement.