Quantum independent-set problem and non-Abelian adiabatic mixing

Journal Article · 12 January 2020 · Physical Review A

DOI: https://doi.org/10.1103/physreva.101.012318 · OSTI ID:1802388

Wu, Biao ^[1]; Yu, Hongye ^[2]; Wilczek, Frank ^[3]

---

1. Peking Univ., Beijing (China); Shanghai Jiao Tong Univ. (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); OSTI
2. Peking Univ., Beijing (China)
3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Shanghai Jiao Tong Univ. (China); Stockholm Univ. (Sweden); Arizona State Univ., Tempe, AZ (United States)

We present an efficient quantum algorithm for independent-set problems in graph theory, based on non- Abelian adiabatic mixing. In this work, we illustrate the performance of our algorithm with analysis and numerical calculations for two different types of graphs, with the number of edges proportional to the number of vertices or its square. Our quantum algorithm is compared to the corresponding quantum circuit algorithms and classical algorithms. Non-Abelian adiabatic mixing can be a general technique to aid exploration in a landscape of near-degenerate ground states.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: European Research Council (ERC); National Key R&D Program of China; National Natural Science Foundation of China (NSFC); Swedish Research Council (VR); USDOE Office of Science (SC)
• Grant/Contract Number: SC0012567
• OSTI ID: 1802388
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 101; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English