Solving independent set problems with photonic quantum circuits

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 , with edges ? being the two-body interactions between adjacent vertices ?. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of . Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem ?(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.

Yao, Xing-Can (författare)
Wu, Biao (författare)
Fei, Yue-Yang (författare)
Mao, Yingqiu (författare)
Zhang, Rui (författare)
Liu, Li-Zheng (författare)
Wang, Zhenduo (författare)
Li, Li (författare)
Liu, Nai-Le (författare)
Wilczek, Frank,1951-Stockholms universitet,Fysikum,Shanghai Jiao Tong University, China; MIT, USA; Arizona State University, USA(Swepub:su)wilczek (författare)
Chen, Yu-Ao (författare)
Pan, Jian-Wei (författare)
Stockholms universitetFysikum (creator_code:org_t)

Ingår i:Proceedings of the National Academy of Sciences of the United States of America120:220027-84241091-6490

Av författaren/redakt...: Yin, Xu-Fei; Yao, Xing-Can; Wu, Biao; Fei, Yue-Yang; Mao, Yingqiu; Zhang, Rui; visa fler...; Liu, Li-Zheng; Wang, Zhenduo; Li, Li; Liu, Nai-Le; Wilczek, Frank, ...; Chen, Yu-Ao; Pan, Jian-Wei; visa färre...

Om ämnet

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.