Understanding the Limitation of Quantum Computation by Quantum Graph Theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 23240001
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: IMAI HIROSHI 東京大学, 情報理工学(系)研究科, 教授 (80183010)
• Co-Investigator(Kenkyū-buntansha): YAMASHITA Shigeru 立命館大学, 情報理工学部, 教授 (30362833) ; MATSUMOTO Keiji 国立情報学研究所, 情報学プリンシプル研究系, 准教授 (60272390)
• Co-Investigator(Renkei-kenkyūsha): MURAO Mio 東京大学, 大学院理学系研究科, 教授 (30322671) ; LE GALL Francois 東京大学, 大学院情報理工学系研究科, 特任准教授 (50584299) ; KAWAMURA Akitoshi 東京大学, 総合文化研究所, 講師 (20600117)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 量子計算理論 / 量子グラフ理論 / 量子コンピュータ / 計算量理論 / グラフマイナー理論

Outline of Final Research Achievements

To understand the limitations of power of quantum computing, researchers in the group collaborated with one another from the point of multi-facet views from computer science to physics, and obtained the following results.

(1) Focusing on Measurement-Based Quantum Computing (MBQC) and other modes for quantum computation with their discrete and physical structures, optimization and transformability on quantum circuits, and .universal measurement schemes were studied. Also, MBQC-universality of Platonic and Archimedean periodic graph were shown. (2) Based on graph vertex-minor theory with rank widths were applied to efficiently computing the partition function of Ising mode. (3) A quantum multi-prover interactive system for quantum Arthur-Merlin game was treated in a unified manner. (4) A new connection of Binary Decision Diagrams (BDD), which have vast applications in computer science, with quantum computing, especially MBQC, was revealed.

Free Research Field

量子情報科学