Solving independent set problems with photonic quantum circuits

Journal Article · Mon May 22 00:00:00 EDT 2023 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2212323120· OSTI ID:1974661

Yin, Xu-Fei ^[1]; Yao, Xing-Can ^[1]; Wu, Biao ^[2]; Fei, Yue-Yang ^[1]; Mao, Yingqiu ^[1]; Zhang, Rui ^[1]; Liu, Li-Zheng ^[1]; Wang, Zhenduo ^[3]; Li, Li ^[1]; Liu, Nai-Le ^[1]; Wilczek, Frank ^[4]; Chen, Yu-Ao ^[1]; Pan, Jian-Wei ^[1]

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1. 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, Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
2. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China, Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
4. Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China, Center for Theoretical Physics, MIT, Cambridge, MA 02139, T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden, Department of Physics and Origins Project, Arizona State University, Tempe, AZ 25287

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 ${\mathcal{H}}_{\mathbf{IS}}^{\mathbf{G}(\mathbf{V},\mathbf{E})}$ , with edges $\mathbf{E}$ being the two-body interactions between adjacent vertices $\mathbf{V}$ . Thus, solving the IS problem is equivalent to finding all the computational basis ground states of ${\mathcal{H}}_{\mathbf{IS}}^{\mathbf{G}(\mathbf{V},\mathbf{E})}$ . Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of ${\mathcal{H}}_{\mathbf{IS}}^{\mathbf{G}(\mathbf{V},\mathbf{E})}$ [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem $\mathbf{G}(8,7)$ 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0012567
• OSTI ID: 1974661
• Alternate ID(s): OSTI ID: 2420214
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 22 Vol. 120; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of Sciences
• Country of Publication: United States
• Language: English