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2004 Fiscal Year Final Research Report Summary

Suppression of decoherence and development of quantum error correcting codes in solid state qubits

Research Project

Project/Area Number 14540346
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 固体物性Ⅱ(磁性・金属・低温)
Research InstitutionKinki University

Principal Investigator

NAKAHARA Mikio  Kinki University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (90189019)

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)
Project Period (FY) 2002 – 2004
Keywordsholonomic quantum computing / decoherence / Cartan decomposition / Josephson junction qubits / NMR quantum computer / isoholonomic problem / quantum information geometry / single-molecule magnet
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.

  • Research Products

    (26 results)

All 2005 2004 2003 2002

All Journal Article (22 results) Book (4 results)

  • [Journal Article] Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation2005

    • Author(s)
      S.Tanimura, M.Nakahara, D.Hayashi
    • Journal Title

      Journal of Mathematical Physics 46

      Pages: 022101 1-022101 15

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Exact solutions of holonomic quantum computation2004

    • Author(s)
      S.Tanimura, D.Hayashi, M.Nakahara
    • Journal Title

      Physics Letters A 325

      Pages: 199-205

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Implementing Shor's algorithm on Josephson charge qubits2004

    • Author(s)
      J.J.Vartiainen, A.O.Niskanen, M.Nakahara, M.M.Salomaa
    • Journal Title

      Physical Review A 70

      Pages: 012319 1-012319 11

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Topological vortex formation in a Bose-Einstein condensate under gravitational field2004

    • Author(s)
      Y.Kawaguchi, M.Nakahara, T.Ohmi
    • Journal Title

      Physical Review A 70

      Pages: 043605 1-043605 6

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Demonstrating quantum algorithm acceleration with NMR quantum computer2004

    • Author(s)
      M.Nakahara, Y.Kondo, K.Hata, S.Tanimura
    • Journal Title

      Physical Review A 70

      Pages: 052319 1-052319 5

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Information Entropy in Cosmology2004

    • Author(s)
      A.Hosoya, T.Buchert, M.Morita
    • Journal Title

      Physical Review Letters 92

      Pages: 141302 1-141302 4

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A novel Mn12 single-molecule magnet with a μ3-methanesulfonate bridge2004

    • Author(s)
      T.Kuroda-Sowa 他6名
    • Journal Title

      Chemistry Letters 33

      Pages: 540-541

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A Mn12 Single-Molecule Magnet [Mn12O12(OAc)12(dpp)4] (dppH=Diphenyl Phosphate) with No Coordinating Water Molecules2004

    • Author(s)
      G.-Q.Bian, T.Kuroda-Sowa 他6名
    • Journal Title

      Inorganic Chemistry 43

      Pages: 4790-4792

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Information Entropy in Cosmology2004

    • Author(s)
      A.Hosoya, I.Buchert, M.Morita
    • Journal Title

      Physical Review Letters 92

      Pages: 141302:1-141302:4

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A novel Mn12 single-molecule magnet with a μ3-methanesulfonate bridge2004

    • Author(s)
      T.Kuroda-Sowa, et al.
    • Journal Title

      Chemistry Letters 33

      Pages: 540-541

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Mn12 Single-Molecule Magnet [Mn12012(OAc)12(dpp)4] (dppH =Diphenyl Phosphate) with No Coordinating Water Molecules2004

    • Author(s)
      G.-Q.Bian, T.Kuroda-Sowa et al.
    • Journal Title

      Inorganic Chemistry 43

      Pages: 4790-4792

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Synthesis, crystal structure and magnetic properties of novel Mn12 singlemolecule magnets with thiophenecarboxylate, [Mn12O12(O2CC4H3S)16(H2O)4], and its tetraphenylphosphonium salt2003

    • Author(s)
      T.Kuroda-Sowa, 他6名
    • Journal Title

      Polyhedron 22

      Pages: 1795-1801

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Acceleration of quantum algorithms using three-qubit gates2003

    • Author(s)
      J.J.Varitainen, A.O.Niskanen, M.Nakahara, M.M.Salomaa
    • Journal Title

      International Journal of Quantum Information 2

      Pages: 1-10

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Synthesis, crystal structure and magnetic properties of novel Mn12 singlemolecule magnets with thiophenecarboxylate, [Mn_<12>O_<12> (O_2CC_4H_3S)_<16>(H_2O)_4], and its tetraphenylphosphonium salt2003

    • Author(s)
      T.Kuroda-Sowa, et al.
    • Journal Title

      Polyhedron 22

      Pages: 1795-1801

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Optimal Holonomic Quantum Gates2002

    • Author(s)
      A.O.Niskanen, M.Nakahara, M.M.Salomaa
    • Journal Title

      Quantum Information and Computation 2

      Pages: 560-577

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Quantum entropy bound by information in black hole space-time2002

    • Author(s)
      A.Hosoya, A.Carlini
    • Journal Title

      Physical Review D 66

      Pages: 104011 1-104011 5

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Naked singularity and thunderbold2002

    • Author(s)
      A.Ishibashi, A.Hosoya
    • Journal Title

      Physical Review D 66

      Pages: 104016 1-104016 6

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Realization of arbitrary gates in holonomic qunatum computation2002

    • Author(s)
      A.O.Niskanen, M.Nakahara, M.M.Salomaa
    • Journal Title

      Physical Review A 67

      Pages: 012319 1-012319 10

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Continuous creation of a vortex in a Bose-Einstein condensate with hyperfine spin F=22002

    • Author(s)
      M.Mottonen, N.Matsumoto, M.Nakahara, T.Ohmi
    • Journal Title

      Journal of Physics : Condensed Matter 14

      Pages: 13481-13491

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A Chemical Modification of a Mn12 Single-Molecule Magnet by Replacing Carboxylate Anions with Diphenylphosphate Anions2002

    • Author(s)
      T.Kuroda-Sowa, 他6名
    • Journal Title

      Chemistry Letters 31

      Pages: 682-683

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Continuous creation of a vortex in a Bose-Einstein condensate with hyperfine spin F=22002

    • Author(s)
      M.Mottonen, N.Matsumoto, M.Nakahara, T.Ohmi
    • Journal Title

      Journal of Physics: Condensed Matter 14

      Pages: 13481-13491

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Chemical Modification of a Mn12 Single-Molecule Magnet by Replacing Carboxylate Anions with Diphenylphosphate Anions2002

    • Author(s)
      T.Kuroda-Sowa, et al.
    • Journal Title

      Chemistry Letters 31

      Pages: 682-683

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Zeta Functions, Topology and Quantum Physics2005

    • Author(s)
      T.Aoki, S.Kanemitsu, M.Nakahara, Y.Ohno(ed)
    • Total Pages
      219
    • Publisher
      Springer, New York
    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Zeta Functions, Topology and Quantum Physics2005

    • Author(s)
      T.Aoki, S.Kanemitsu, M.Nakahara, Y.Ohno (ed.)
    • Total Pages
      219
    • Publisher
      Springer, New York
    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Geometry, Topology and Physics(2nd.ed.)2003

    • Author(s)
      Mikio Nakahara
    • Total Pages
      573
    • Publisher
      IOP Publishing, Bristol
    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Geometry, Topology and Physics (2nd edn.)2003

    • Author(s)
      Mikio Nakahara
    • Total Pages
      573
    • Publisher
      IOP Publishing, Bristol
    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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