Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.
Proc Natl Acad Sci U S A. 2023 May 30;120(22):e2212323120. doi: 10.1073/pnas.2212323120. Epub 2023 May 22.
An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, ., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph (, ) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.
独立集（IS）是图中的顶点集合，其中没有边连接任意两个顶点。在绝热量子计算中[E. Farhi 等，Science 292, 472-475 (2001)；A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)]，给定的图（，）可以自然地映射到一个多体哈密顿量[公式：见文本]，其中边[公式：见文本]是相邻顶点[公式：见文本]之间的二体相互作用。因此，解决 IS 问题相当于找到[公式：见文本]的所有计算基态。最近，非阿贝尔绝热混合（NAAM）已被提出用于解决这个任务，利用[公式：见文本]的一个新兴非阿贝尔规范对称性[B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]。在这里，我们通过使用由三个 C-Phase 门、四个确定性两量子比特门阵列（DGA）和十个单旋转门组成的线性光学量子网络，对具有代表性的 IS 问题[公式：见文本]进行数字模拟，成功地解决了该问题。通过足够的 Trotterization 步骤和精心选择的演化路径，成功地识别出了最大的 IS。值得注意的是，我们发现 IS 的总概率为 0.875(16)，其中非平凡的 IS 具有相当大的权重约 31.4%。我们的实验证明了 NAAM 在解决 IS 等效问题方面的潜在优势。
