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研究生： 沈恩照
Shen, En-Chao
論文名稱： Optimal Construction of Quantum Circuits
量子線路之最佳建構
指導教授： 余怡德
Yu, Ite
蘇正耀
Su, Zheng-Yao
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2009
畢業學年度： 98
語文別： 英文
論文頁數： 57
中文關鍵詞： 量子線路
外文關鍵詞： Cartan decomposition, Systematic
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    • In this thesis, a systematic and comprehensive method is reported to obtain all factorizations of a quantum circuit. The result is obtained by searching all Cartan decompositions in a structure called quotient-algebra partition and taking all decomposition paths into consideration. Accordingly, the optimal construction requiring the minimum number of CNOTs for an arbitrary quantum circuit is achieved.

    1. Overview 2. Formalism 2.1 Cartan decomposition 2.2 s-Representation 2.3 Quotient-algebra partition 2.4 Recursive Cartan decomposition 2.5 Consideration of all ranks 2.6 Decomposition sequence 3. Tren of optimal paths 3.1 Permutation process 3.2 Consideration of all decomposition levels 4. The general form of optimal paths 4.1 Top-down algorithm 4.2 Two types of reduction 4.3 The bottom-up algorithm 4.4 Optimal decomposition without reduction 4.5 Total number of CNOTs of a recursive decomposition sequence 5. Optimal decomposition with reduction 5.1 Algorithm of reduction 5.2 An example 5.3 Decomposition sequence determined in the quotient-algebra partition other than {P_Q(\widetilde{B}^{[r]} )} 5.4 Discussion 5.5 Conclusion Reference Appendix

    Quotient Algebra and Cartan Decomposition for su(N) I, Zheng-Yao Su; quant-ph/0603190 22 Mar 2006.

    Quotient Algebra and Cartan Decomposition for su(N) II, Zheng-Yao Su and Ming-chung Tsai, to appear.

    Quotient Algebra and Cartan Decomposition for su(N) III, Zheng-Yao Su and Ming-chung Tsai, to appear.

    Quotient Algebra and Cartan Decomposition for su(N) IV, Zheng-Yao Su and Ming-chung Tsai, to appear.

    Quotient Algebra and Cartan Decomposition for su(N) V, Zheng-Yao Su and Ming-chung Tsai, to appear.

    Navin Khaneja, et al. Phys. Rev. A. 63 , 032308 (2001).

    Farrokh Vatan, et al. Phys. Rev. A 69, 032315 (2004).

    Synthesis of Quantum Logic Circuits, Vivik V. Shende et al.(2006), quant-ph/0406176

    Constructive Quantum Shannon Decomposition from Cartan Involutions, Byron Drury, Peter Love; quant-ph 0806.4015 jun 2008.

    Realization of a General Three-Qubit Quantum Gate, Farrokh Vatan and Colin P. Williams; quantph/0401178 30 Jan 2004.

    Approximation by Quantum Circuits, E.Knill, quant-ph/9508006.

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