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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
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsholonomic quantum computing / decoherence / Cartan decomposition / Josephson junction qubits / NMR quantum computer / isoholonomic problem / quantum information geometry / single-molecule magnet / エンタングルメント / 量子情報空間の計量 / 量子計算 / 量子情報 / 量子ゲート / 量子アルゴリズム加速 / ホロノミー / NMR / 量子ビット / 量子ドット / 液体ヘリウム上の電子
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.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (43 results)

All 2005 2004 2003 2002 Other

All Journal Article (28 results) Book (5 results) Publications (10 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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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 Vol.46 No.2

    • Related Report
      2004 Annual Research Report
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Information Entropy in Cosmology2004

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

      Physical Review Letters 92

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Information Entropy in Cosmology2004

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

      Physical Review Letters 92

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Acceleration of quantum algorithms using three-qubit gates2004

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

      International Journal of Quantum Information Vol.2 No.1

      Pages: 1-10

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Implementing Shor's algorithm on Josephson charge qubits2004

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

      Physical Review A Vol.70,No.1

    • Related Report
      2004 Annual Research Report
  • [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 Vol.70,No.5

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Information Entropy in Cosmology2004

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

      Physical Review Letters Vol.92 No.14

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Mn12 single-molecule magnet [Mn12O12(OAc)12(dpp)4] (dppH=diphenylphosphate) with no coordinating water molecules2004

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

      Inorganic Chemistry Vol.43

      Pages: 4790-4792

    • Related Report
      2004 Annual Research Report
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum entropy bound by information in black hole space-time2002

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

      Physical Review D 66

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Naked singularity and thunderbold2002

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

      Physical Review D 66

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [Book] Zeta Functions, Topology and Quantum Physics2005

    • Author(s)
      T.Aoki, S.Kanemitsu, M.Nakahara, Y.Ohno eds.
    • Total Pages
      219
    • Publisher
      Springer Verlag
    • Related Report
      2004 Annual Research Report
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [Publications] Juha Varitainen, Antti Niskanen, Mikio Nakahara, Martti Salomaa: "Acceleration of quantum algorithms using three-qubit gates"International Journal of Quantum Information. 2,No.1(印刷中). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Hosoya, T.Buchert, M.Morita: "Information Entropy in Cosmology"Physical Review Letters. 印刷中. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Kuroda-Sowa, T.Nogami, H.Konaka, M.Maekawa, M.Munakata, H.Miyasaka, M.Yamashita: "Synthesis, crystal structure and magnetic properties of novel Mn_<12> single-molecule magnets with thiophenecarboxylate,[Mn_<12>O_<12>(O_2CC_4H_3S)_<16>(H_2O)_4], and its tetraphenylphosphonium salt"Polyhedron. 22. 1795-1801 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Kuroda-Sowa, T.Handa, T.Kotera, M.Maekawa, M.Munakata, H.Miyasaka, M.Yamashita: "A novel Mn_<12> single-molecule magnet with a 3-methanesulfonate bridge"Chem. Lett.. 33(印刷中). (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Mikio Nakahara: "Geometry, Topology and Physics(2nd ed)"Institute of Physics Publishing, Bristol. 573 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.O.Niskanen, M.Nakahara, M.M.Salomaa: "Realization of arbitrary gates in holonomic qunatum computation"Physical Review A. 67・1. 012319-1-012319-10 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.O.Niskanen, M.Nakahara, M.M.Salomaa: "Optimal Holonomic Quantum Gates"Quantum Information and Computation. 2・Special Issue. 560-577 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Mottonen, N.Matsumoto, M.Nakahara, T.Ohmi: "Continuous creation of a vortex in a Bose-Einstein condensate with hyperfine spin F=2"Journal of Physics : Condensed Matter. 14・49. 13481-13491 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Hosoya, A.Carlini: "Quantum entropy bound by information in black hole spacetime"Physical Review D. 66・10. 104011-1-104011-5 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Kuroda-Sowa, S.Fukuda, S.Miyoshi, M.Maekawa, M.Munakata, H.Miyasaka, M.Yamashita: "A Chemical Modification of a Mn_<12> Single-Molecule Magnet by Replacing Carboxylate Anions with Diphenylphosphate Anions"Chemistry Letters. 31・7. 682-683 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2020-05-15  

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