In:
Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, Vol. 120, No. 22 ( 2023-05-30)
Abstract:
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, et al ., Science 292, 472–475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061–1081 (2008)], a given graph G ( V , E ) can be naturally mapped onto a many-body Hamiltonian H IS G ( V , E ) , with edges E being the two-body interactions between adjacent vertices V . Thus, solving the IS problem is equivalent to finding all the computational basis ground states of H IS G ( V , E ) . Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of H IS G ( V , E ) [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem G ( 8 , 7 ) 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.
Type of Medium:
Online Resource
ISSN:
0027-8424
,
1091-6490
DOI:
10.1073/pnas.2212323120
Language:
English
Publisher:
Proceedings of the National Academy of Sciences
Publication Date:
2023
detail.hit.zdb_id:
209104-5
detail.hit.zdb_id:
1461794-8
SSG:
11
SSG:
12
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