2004 Fiscal Year Final Research Report Summary
Suppression of decoherence and development of quantum error correcting codes in solid state qubits
| Project/Area Number |
14540346
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
固体物性Ⅱ(磁性・金属・低温)
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| Research Institution | Kinki University |
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Principal Investigator |
NAKAHARA Mikio Kinki University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (90189019)
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| Co-Investigator(Kenkyū-buntansha) |
HOSOYA Akio Tokyo Institute of Technology, Graduate School of Science and Engineering, Professor, 理工学研究科, 教授 (80028258)
KONDO Yasushi Kinki University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (40330229)
KURODA Takayoshi Kinki University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (80257964)
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| Project Period (FY) |
2002 – 2004
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| Keywords | holonomic quantum computing / decoherence / Cartan decomposition / Josephson junction qubits / NMR quantum computer / isoholonomic problem / quantum information geometry / single-molecule magnet |
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| Research Abstract |
Nakahara and his Finnish collaborators developed a method for efficient implementation of quantum algorithms utilizing multi-qubit modules. This strategy has been employed for holonomic quantum computation first and subsequently applied to a more realistic Josephson junction qubit system. It has been estimated how many qubits and computational steps are required to factorize 21 using three-qubit modules. Later Tanimura of Osaka City University and Nakahara solved the isoholonomic problem exactly in the idealized siuation, where the relevant fibre bundle is the Stiefel manifold over the Grassmann manifold. This solves the longstanding isoholonomic problem posed by Montgomery in 1991.
Nakahara and Kondo built an NMR quantum computer at Kinki University. Nakahara, with Tanimura, obtained time-optimal solutions for quantum algorithms, utilizing the Cartan decomposition of a Lie group, and Kondo executed these solutions on the NMR quantum computer with two-qubit molecules. It was verified experimentally that the NMR spectrum is improved thanks to reductions in execution time and the number of gates. It was also pointed out that a quantum algorithm U may be accelerated by adding a properly chosen simple extra gate W to U so that the algorithm now becomes WU. This is again verified experimentally on the NMR quantum computer and improvement in spectrum has been observed. This technique is called the warp-drive while the gate W is called the warp-gate.
Hosoya studied the Hawking radiation in the blackhole spacetime from quantum information point of view and analyzed the entropy change when a measurement instrument is thrown into a blackhole after a measurement is made. He also studied the metric in quantum information geometry.
Kuroda analyzed the chemical properties of a single-molecule magnet, Mn12 complex, which might work as a qudit, a quantum system with d states.
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