現実的な状況下での量子計算の能力に関する研究

• Project/Area Number: 16092218
• Research Category: Grant-in-Aid for Scientific Research on Priority Areas
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Nara Institute of Science and Technology
• Principal Investigator: 山下 茂 Nara Institute of Science and Technology, 情報科学研究科, 准教授 (30362833)
• Co-Investigator(Kenkyū-buntansha): 中西 正樹 奈良先端科学技術大学院大学, 情報科学研究科, 助教 (40324967)
• Project Period (FY): 2004 – 2007
• Project Status: Completed (Fiscal Year 2007)
• Budget Amount: ¥6,700,000 (Direct Cost: ¥6,700,000); Fiscal Year 2007: ¥1,700,000 (Direct Cost: ¥1,700,000); Fiscal Year 2006: ¥1,700,000 (Direct Cost: ¥1,700,000); Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000); Fiscal Year 2004: ¥1,700,000 (Direct Cost: ¥1,700,000)
• Keywords: 量子回路設計 / 多準位量子ゲート / Cosine-Sine分解 / Linear Nearest Neighbor / 量子回路の等価性判定 / 量子計算 / 量子封印 / Pure Dephaing / エラー回復 / 量子秘密分散 / Quantum Sealing / 量子秘密通信 / 量子分散アルゴリズム / 量子オートマトン / 量子オラクル計算 / 量子分散計算 / 量子プログラミング / 量子通信量 / 量子プッシュダウンオートマトン

Research Abstract

本研究では、将来の量子計算機の有効な利用のために、様々な状況下での量子計算の能力の解析や利用方法に関しての研究を行っている。今年度は昨年度からの種々の研究を継続し、以下のような研究成果へと発展させた。
1.量子回路は一般に2準位で考えられているが、物理的な実現を考えると多準位系を用いたほうが現実的となる場合もあると考えられる。そこで多準位系の量子ゲートによる量子回路設計のために、与えられた任意のn次元のユニタリ行列を効率よく基本量子ゲートの積に変換する手法を考奏した。具体的には、従来からあるCosine-Sine分解における分割のサイズを適切に調整することにより、ある程度の規模の入力数ならば従来手法よりも少ない基本ゲート数で与えられたユニタリ行列を分解することができることを示した。
2.現在最も実現の可能性が高いと考えられている量子計算の実現モデルである、Linear Nearest Neighbor(LNN)アーキテクチャ上で、与えられた任意の量子回路を効率よく実行することが量子計算の実現には重要となると考えられる。そこで、任意の量子回路をLNNアーキテクチャ上で実現できるようにSWAPゲートを挿入して回路を変換する手法を考案した。提案手法は、ナイーブな手法に比べて少ない計算時間でSWAPゲートの数を削減することができ、また、今までに報告されている人手で設計された回路をより少ないSWAPゲート数でのLNN上の量子回路へ変換できる。
3.人手で量子回路を設計するときにLNNへの変換などを行うが、その際に予期せぬ間違いをすることがある。そのため、従来の回路設計と同様に、変換の前後の回路の等価性判定が重要となる。量子回路の等価性判定のために、ReversibleMiterと呼ばれる等価性判定を行うための回路を提案した。さらに、量子回路の等価性判定ツールQuIDDProと従来の回路の等価性判定ツールABCをReversibleMiterに組み合わせて、従来手法よりも高速に等価性判定を行う手法を考案した。

Research Products

• [Journal Article] Synthesis of quantum circuits for d-level systems by using Cosine-Sine decomposition (2009)
  • Author(s): Y. Nakajima
  • Journal Title: Quantum Information and Computation (採録決定)
  • Peer Reviewed
• [Journal Article] Multi-Party Quantum Communication Complexity with Routed Messages (2009)
  • Author(s): S. Tani
  • Journal Title: IEICE transactions on Information and Systems E92-D Pages: 191-199
  • Peer Reviewed
• [Journal Article] DDMF : An Efficient Decision Diagram Structure for Design Verification of Quantum Circuits under a Practical Restriction (2008)
  • Author(s): S. Yamashita
  • Journal Title: IEICE Trans. Fundamentals E91-A Pages: 3793-3802
  • NAID: 10026854528
  • Peer Reviewed
• [Journal Article] Quantum Network Coding (2007)
  • Author(s): M.Hayashi
  • Journal Title: Proc. of the 24th International Symposium on Theore tical Aspects of Computer Science STACS 2007 Pages: 610-611
• [Journal Article] Robust Quantum Algorithms Computing OR with e-biased Oracles (2007)
  • Author(s): T.Suzuki
  • Journal Title: IEICE transactions on Information and Systems Vol. E90-D, No.2 Pages: 395-402
• [Journal Article] Improved Algorithms for Quantum Identification of Boolean Oracles (2007)
  • Author(s): A.Ambainis
  • Journal Title: Theoretical Computer Science (掲載予定)
• [Journal Article] (4, 1)-Quantum Random Access Coding Does Not Exist (2006)
  • Author(s): M.Hayashi
  • Journal Title: IEICE Technical Report COMP2006-14 Pages: 33-38
• [Journal Article] 量子状態を送信可能な量子秘密通信プロトコル (2006)
  • Author(s): 村上ユミコ
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2006-28 Pages: 133-134
• [Journal Article] 3準位量子ゲート設計のためのユニタリ行列近似 (2006)
  • Author(s): 西山寛之
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2006-41 Pages: 180-183
• [Journal Article] (4, 1)-Quantum Random Access Coding Does Not Exist (2006)
  • Author(s): M.Hayashi
  • Journal Title: Proc. of the 2006 IEEE International Symposium on Information Theory ISIT2006 Pages: 446-450
• [Journal Article] (4, 1)-Quantum Random Access Coding Does Not Exist-One Qubit Is Not Enough To Re cover One of Four Bits (2006)
  • Author(s): M.Hayashi
  • Journal Title: New J. Phys. 8 Pages: 129-129
• [Journal Article] Robust Quantum Algorithms with e-biased Oracles (2006)
  • Author(s): T.Suzuki
  • Journal Title: Proc. of 12th Annual International Computing and Combinatorics Conference COCOON2006 Pages: 116-125
• [Journal Article] An Efficient Approximation of SU(d) Using Decomposition (2006)
  • Author(s): H.Nishiyama
  • Journal Title: Proc. of Asian Conference on Quantum Information Science 2006 AQIS2006 Pages: 147-148
• [Journal Article] Quantum Secure Direct Communication Protocols for Sending a Quantum State (2006)
  • Author(s): Y.Murakami
  • Journal Title: 2006 International Symposium on Information Theory and its Applications ISITA2006(CD-ROM)
• [Journal Article] 量子封印を用いた量子認証 (2006)
  • Author(s): 竹谷昌敏
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2006-92 Pages: 209-212
• [Journal Article] Pure Dephasingを考慮した量子オラクル計算モデル (2006)
  • Author(s): 山下茂
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2006-97 Pages: 229-232
• [Journal Article] 量子文字列封印における復号化率と検出率のトレードオフについて (2006)
  • Author(s): 中西正樹
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2006-98 Pages: 233-236
• [Journal Article] Decision Diagram Data Structure to Represent Quantum Circuit (2006)
  • Author(s): S.Yamashita
  • Journal Title: IEICE Technical Report VLD2006-58 Pages: 41-46
  • NAID: 110005717335
• [Journal Article] Quantum communication complexity for the distinctness function on a ring (2006)
  • Author(s): S.Tani, M.Nakanishi, S.Yamashita
  • Journal Title: Workshop on Theory of Quantum Computation Communication and Cryptography 2006 TQC2006 Pages: 10-11
• [Journal Article] Expressive power of guantum pushdown automata with classical stack operations under the perfect-soundness conditions (2006)
  • Author(s): M.Nakanishi, K.Hamaguchi, T.Kashiwabara
  • Journal Title: IEICE Transactions on Information and Systems Vol.E89-D, no.3 Pages: 1120-1127
• [Journal Article] No preshared key quantum secret communication protocol (2006)
  • Author(s): Y.Murakami, M.Nakanishi, S.Yamashita, K.Watanabe
  • Journal Title: 電子情報通信学会2006年総合大会講演論文集
• [Journal Article] Upper bounds or quantum biased oracles with explicit bias rate (2006)
  • Author(s): T.Suzuki, S.Yamashita, M.Nakanishi, K.Watanabe
  • Journal Title: LA Symposium
• [Journal Article] Quantum Sampling for Balanced Allocations (2005)
  • Author(s): K.Iwama, A.Kawachi, S.Yamashita
  • Journal Title: IEICE transactions on Information and Systems Vol.E88-D No.1 Pages: 39-46
  • NAID: 110003214133
• [Journal Article] Explicit implementation of quantum circuits on a quantum-dot-cellular-automata-like architecture (2005)
  • Author(s): Y.Kawano, S.Yamashita, M.Kitagawa
  • Journal Title: Physical Review A Vol.72 No.1 Pages: 12301-12301
• [Journal Article] Quantum Biased Oracles (2005)
  • Author(s): K.Iwama, A.Kawachi, S.Yamashita
  • Journal Title: Journal of IPSJ Vol.46 No.10 Pages: 2400-2408
  • NAID: 130000058403
• [Journal Article] Automata with quantum and classical resources (2005)
  • Author(s): M.Nakanishi
  • Journal Title: TPSJ Journal Vol.46, no.10 Pages: 2384-2391
  • NAID: 130000058402
• [Journal Article] Quantum versus classical pushdown automata in exact computation (2005)
  • Author(s): Y.Murakami, M.Nakanishi, S.Yamashita, K.Watanabe
  • Journal Title: IPSJ Journal Vol.46, no.10 Pages: 2471-2480
  • NAID: 130000022371
• [Journal Article] Quantum sealing schemes against collective measurement attacks (2005)
  • Author(s): T.Katsumata, M.Nakanishi, S.Yamashita, K.Watanabe
  • Journal Title: IEICE Technical Report, QIT2005-90 Pages: 229-232
• [Journal Article] Cheater identifiable quantum secret sharing schemes (2005)
  • Author(s): Y.MuraKami, M.Nakanishi, S.Yamashita, K.Watanabe
  • Journal Title: IEICE Technical Report, QIT2005-55 Pages: 89-82
  • NAID: 110003298621
• [Journal Article] General Bounds for Quantum Biased Oracles (2005)
  • Author(s): K.Iwama, R.Raymond, S.Yamashita
  • Journal Title: Journal of IPSJ Vol.46 No.10 Pages: 2481-2491
  • NAID: 130000022370
• [Journal Article] Toward a Practical Environment for Quantum Programming (2005)
  • Author(s): S.Yamashita, M.Nakanishi, K.Watanabe
  • Journal Title: Asia-Pacific Conference on Quantum Information Science APCQIS 2004(印刷中)
• [Journal Article] Robust Quantum Algorithms for Oracle Identification (2005)
  • Author(s): K.Iwama, A.Kawachi, R.Raymond, H.P., S.Yamashita
  • Journal Title: Workshop on Quantum Information Processing 2005 QIP2005
  • NAID: 110002812017
• [Journal Article] Quantum Protocol for the List-nonequality Function (2005)
  • Author(s): S.Tani, M.Nakanishi, S.Yamashita
  • Journal Title: Workshop on Quantum Information Processing 2005 QIP2005
• [Journal Article] オラクル同定問題に対する頑健な量子アルゴリズム (2004)
  • Author(s): 河内亮周, 山下茂, 岩間一雄
  • Journal Title: 情報処理学会研究会報告アルゴリズム研究会 Vol.96-1 Pages: 1-8
  • NAID: 110002812017
• [Journal Article] On the Power of One-Sided Error Quantum Pushdown Automata with Classical Stack Operations (2004)
  • Author(s): M.Nakanishi
  • Journal Title: Proc.of 10th Annual International Computing and Combinatorics Conference (COCOON 2004) LNCS 3106 Pages: 179-187
• [Journal Article] リスト型非等価関数を計算する量子プロトコル (2004)
  • Author(s): 谷誠一郎, 中西正樹, 山下茂
  • Journal Title: 電子情報通信学会量子情報技術研究会 QIT2004-51 Pages: 21-25
• [Presentation] An Efficient Method to Convert Arbitrary Quantum Circuits to Ones on a Linear Nearest Neighbor Architecture (2009)
  • Author(s): Y. Hirata
  • Organizer: The Third International Conference on^ Quantum, Nano and Micro Technologies
  • Place of Presentation: Fiesta Americana Condes a Cancun (メキシコ)
  • Year and Date: 2009-02-02
• [Presentation] Average/Worst-Case Gap of Quantum Query Complexities (2009)
  • Author(s): S. Tani
  • Organizer: The Twelfth Workshop on Quantum Information Processing
  • Place of Presentation: Santa Fe Convention Center (アメリカ)
  • Year and Date: 2009-01-14
• [Presentation] Quantum Query Complexity of Boolean Functions with Small On-Sets (2008)
  • Author(s): S. Tani
  • Organizer: The 19th International Symposium on Algorithms and Computation
  • Place of Presentation: Gold Coast International Hotel (オーストラリア)
  • Year and Date: 2008-12-17
• [Presentation] An Efficient Verification of Quantum Circuits under a Practical Restriction (2008)
  • Author(s): S. Minato
  • Organizer: IEEE 8th International Conference on Computer and Information Technology
  • Place of Presentation: University of Technology (オーストラリア)
  • Year and Date: 2008-07-08
• [Presentation] Multi-Party Quantum Communication Complexity with Routed Messages (2008)
  • Author(s): S. Tani
  • Organizer: 14th Annual International Computing and Combinatorics Conference
  • Place of Presentation: Mercure Teda Dalian Hotel (中国)
  • Year and Date: 2008-06-27
• [Presentation] Equivalence-checking for Reversible Circuits (2008)
  • Author(s): S. Yamashita
  • Organizer: IEEE International Workshop on Logic Synthesis
  • Place of Presentation: Granlibakken Lodgg(アメリカ)
  • Year and Date: 2008-06-04
• [Presentation] An almost optimal quantum string sealing protocol and its security analysis (2008)
  • Author(s): M. Nakanishi
  • Organizer: The 2nd AAAC Annual Meeting AAAC09
  • Place of Presentation: Hangzhou Huajia SHAN Resort (中国)
  • Year and Date: 2008-04-26
• [Presentation] 耐故障性量子計算におけるエラー訂正回数の削減手法 (2008)
  • Author(s): 本間知教
  • Organizer: 電子情報通信学会2008年総合大会
  • Place of Presentation: 北九州学術研究都市 三大学
  • Year and Date: 2008-03-18
• [Presentation] A quantum secure direct communication protocol for sending a quantum state and its security analysis (2008)
  • Author(s): Y. Murakami
  • Organizer: The 2008 Symposium on Cryptography and Information Security
  • Place of Presentation: フェニックス・シーガイア・リゾート(宮崎市)
  • Year and Date: 2008-01-23
• [Presentation] Unbounded-error classical and quantum communication complexity (2007)
  • Author(s): Rudy Raymond
  • Organizer: ISAAC2007
  • Place of Presentation: Sendai Excel Hotel (仙台市)
  • Year and Date: 2007-12-17
• [Presentation] A quantum secure direct communication protocol for sending a quantum state and its security analysis (2007)
  • Author(s): Y. Murakami
  • Organizer: 6th WSEAS International Conference on Information Security and Privacy
  • Place of Presentation: Puerto De La Cruz, Tenerife, Canary Islands, Spain
  • Year and Date: 2007-12-14
• [Presentation] An information-theoretic security analysis of quantum string sealing (2007)
  • Author(s): M. Nakanishi
  • Organizer: 6th WSEAS International Conference on Information Security and Privacy
  • Place of Presentation: Puerto De La Cruz, Tenerife, Canary Islands, Spain
  • Year and Date: 2007-12-14
• [Presentation] An analysis of quantum communication complexity depending on network topologies (2007)
  • Author(s): S. Tani
  • Organizer: 電子情報通信学会 量子情報技術研究会
  • Place of Presentation: 山陽新聞本社さん太ホール(岡山市)
  • Year and Date: 2007-11-21
• [Presentation] A Practical Framework to Utilize Quantum Search (2007)
  • Author(s): S. Yamashita
  • Organizer: 2007 IEEE Congress on Evolutionary Computation
  • Place of Presentation: Swissotel (シンガポール)
  • Year and Date: 2007-09-25
• [Presentation] Unbounded-Error One-way Classical and Quantum Communication Complexity (2007)
  • Author(s): Rudy Raymond
  • Organizer: ICALP 2007
  • Place of Presentation: Wroclaw (Poland)
  • Year and Date: 2007-07-09
• [Patent(Industrial Property Rights)] 特許権 (2006)
  • Inventor(s): 村上 ユミコ, 中西 正樹, 山下 茂
  • Industrial Property Rights Holder: 奈良先端科学技術大学院大学
  • Industrial Property Number: 2006-059933
  • Filing Date: 2006-03-06
• [Patent(Industrial Property Rights)] 量子コンピュータを含むコンピュータシステムのためのプログラム開発支援装置、およびシミュレーション装置 (2004)
  • Inventor(s): 山下 茂
  • Industrial Property Rights Holder: 奈良先端科学技術大学院大学
  • Industrial Property Number: 2004-356175
  • Filing Date: 2004-12-09