We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense random graphs G, numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size α(G) in low polynomial time. The best classical algorithms, by contrast, produce independent sets of size about half of α(G) in polynomial time.

中文翻译：

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逼近最大独立集的量子算法

我们提出了一种基于简并基态的亚希尔伯特空间中的量子非阿贝尔绝热混合来逼近图的最大独立集的量子算法，该算法在次级哈密顿量中产生量子退火。对于稀疏和密集的随机图G，数值模拟表明我们的算法在低多项式时间内平均找到接近最大大小α ( G ) 的独立大小集。相比之下，最好的经典算法在多项式时间内产生大小约为α ( G ) 一半的独立集合。