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Solving independent set problems with photonic quantum circuits.
- Source :
-
Proceedings of the National Academy of Sciences of the United States of America . 5/30/2023, Vol. 120 Issue 22, p1-8. 28p. - Publication Year :
- 2023
-
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 HG(V,E)IS, 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 HG(V,E)IS. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of HG(V,E)IS [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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00278424
- Volume :
- 120
- Issue :
- 22
- Database :
- Academic Search Index
- Journal :
- Proceedings of the National Academy of Sciences of the United States of America
- Publication Type :
- Academic Journal
- Accession number :
- 164142792
- Full Text :
- https://doi.org/10.1073/pnas.2212323120