Zhao Xianjue, Ge Peiyun, Yu Hongye, You Li, Wilczek Frank, Wu Biao
International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China.
Natl Sci Rev. 2025 Jul 29;12(9):nwaf304. doi: 10.1093/nsr/nwaf304. eCollection 2025 Sep.
We compare two quantum Hamiltonian algorithms that address the maximum independent set problem: one based on the emergent non-Abelian gauge matrix in adiabatic evolution of an energetically isolated manifold of states; the other based on designed application of single-qubit operations. We demonstrate that they are mathematically equivalent in the sense that one is the other's interaction picture. Despite their mathematical equivalence, our numerical simulations show significant differences between them in performance, which is explained analytically. Intriguingly, this equivalence unveils that the PXP model, recently prominent in quantum dynamics research, can be viewed as quantum diffusion over the median graph of all independent sets governed by the non-Abelian gauge matrix.
一种基于能量孤立态流形绝热演化中出现的非阿贝尔规范矩阵；另一种基于单量子比特操作的设计应用。我们证明，从一种算法是另一种算法的相互作用绘景的意义上来说，它们在数学上是等价的。尽管它们在数学上等价，但我们的数值模拟表明它们在性能上存在显著差异，对此我们进行了分析解释。有趣的是，这种等价性揭示了最近在量子动力学研究中备受瞩目的PXP模型，可以被视为由非阿贝尔规范矩阵控制的所有独立集的中位数图上的量子扩散。
