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受到Lanyon等(Lanyon B P et al 2008 Nature Physics. 5 134)利用高维Hilbert空间成功简化Toffoli门的启发, 本文将辅助维度应用到普适量子线路中, 结合Cosine-Sine Decomposition(CSD), Quantum Shannon Decomposition(QSD)等矩阵分解方法, 优化了两比特和三比特普适幺正量子线路, 给出了计算n比特普适量子线路复杂度的公式, 并利用线性光学和腔QED系统设计了实验方案. 结果表明, 两比特和三比特量子线路的复杂度已分别接近和优于目前最优结果, 且随着比特数的增加, 本方案的优势愈加明显.Inspired by Lanyon (B. P. Lanyon et al. 2008 Nature Physics. 5 134) successfully simplifying the three-qubit Toffoli gate, we present a novel scheme that optimizes universal quantum logic circuits using assisted higher-dimensional Hilbert space. We construct a more efficient two-qubit circuit and a more effective three-qubit universal quantum circuit by using assisted dimension, Cosine-Sine Decomposition (CSD) and Quantum Shannon Decomposition (QSD). Meanwhile, we present the formula for the complexity of arbitrary n-qubit universal quantum gate. We propose the physical implementation of this scheme by linear optical circuits and cavity-QED. The results show that the two-qubit and three-qubit universal quantum circuits are respectively close and superior to the current optimal scheme in complexity. And with the increase of the number of qubits, the advantage of our scheme will become increasingly prominent.
[1] Barenco A, Bennett C, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J A, Weinfurter H 1995 Phys. Rev. A 52 3457
[2] Cybenko G 2001 Comp. in Sci. and Engin. 3 27
[3] Golub G H, Van Loan C F 1996 Matrix Computations (3rd ed) (Baltimore: The Johns Hopkins University Press) p223
[4] Knill E 1995 Approximation by quantum circuits LANL report LAUR-95-2225
[5] Aho A V, Svore K M e-print, quant-ph/0311008[2003]
[6] Vartianinen J J, Möttönen M, Salomaa M M 2004 Phys. Rev. Lett. 92 177902
[7] Shende V V, Bullock S S, Markov I L 2006 IEEE Trans. on Computer-Aided Design. 25 1000
[8] Möttönen M, Vartiainen J J, Bergholm V, Salomaa M M 2004 Phys. Rev. Lett. 93 130502
[9] Bergholm V, Vartiainen J J, Möttönen M, Salomaa M M 2005 Phys. Rev. A. 71 052330
[10] Tucciv R R e-print, quant-ph/9805015 [1998]
[11] Möttönen M, Juha J V quant-ph/0504100 [2005]
[12] Shende V V, Markov I L, Bullock S S 2004 Phys. Rev. A. 69 062321
[13] Hanneke D, Home J P, Jost J D, Amini J M, Leibfried D, Wineland D J, 2009 Nature Physics 6 13
[14] Ralph T C, Resch K J, Gilchrist A 2007 Phys. Rev. A 75 022313
[15] Lanyon B P, Barbier M, Almeida M P, Jennewein T, Ralph T C, Resch K J, Pryde G J, O'Brien J L, Gilchrist A, White A G 2008 Nature Physics 5 134
[16] Preskill J 2001 Quantum Information and Computation (Ft.Belvoir: Defense Acquisition University Press) p250
[17] Ralph T C, Langford N K, Bell T B, White A G 2002 Phys. Rev. A 65 062324
[18] Chen G, Church D A, Englert B G, Henkel C, Rohwedder B, Scully M O, Zubairy M S 2007 Quantum Computing Devices Principles, Designs, and Analysis (1st ed) (Boca Raton: Chapman & Hall/CRC) p347
[19] Duan L M, Kimvle H J 2004 Phys. Rev. Lett. 92 127902
[20] Lin Xiumin 2005 PH.D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [林秀敏 2005 博士学位论文 (合肥:中国科学技术大学)]
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[1] Barenco A, Bennett C, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J A, Weinfurter H 1995 Phys. Rev. A 52 3457
[2] Cybenko G 2001 Comp. in Sci. and Engin. 3 27
[3] Golub G H, Van Loan C F 1996 Matrix Computations (3rd ed) (Baltimore: The Johns Hopkins University Press) p223
[4] Knill E 1995 Approximation by quantum circuits LANL report LAUR-95-2225
[5] Aho A V, Svore K M e-print, quant-ph/0311008[2003]
[6] Vartianinen J J, Möttönen M, Salomaa M M 2004 Phys. Rev. Lett. 92 177902
[7] Shende V V, Bullock S S, Markov I L 2006 IEEE Trans. on Computer-Aided Design. 25 1000
[8] Möttönen M, Vartiainen J J, Bergholm V, Salomaa M M 2004 Phys. Rev. Lett. 93 130502
[9] Bergholm V, Vartiainen J J, Möttönen M, Salomaa M M 2005 Phys. Rev. A. 71 052330
[10] Tucciv R R e-print, quant-ph/9805015 [1998]
[11] Möttönen M, Juha J V quant-ph/0504100 [2005]
[12] Shende V V, Markov I L, Bullock S S 2004 Phys. Rev. A. 69 062321
[13] Hanneke D, Home J P, Jost J D, Amini J M, Leibfried D, Wineland D J, 2009 Nature Physics 6 13
[14] Ralph T C, Resch K J, Gilchrist A 2007 Phys. Rev. A 75 022313
[15] Lanyon B P, Barbier M, Almeida M P, Jennewein T, Ralph T C, Resch K J, Pryde G J, O'Brien J L, Gilchrist A, White A G 2008 Nature Physics 5 134
[16] Preskill J 2001 Quantum Information and Computation (Ft.Belvoir: Defense Acquisition University Press) p250
[17] Ralph T C, Langford N K, Bell T B, White A G 2002 Phys. Rev. A 65 062324
[18] Chen G, Church D A, Englert B G, Henkel C, Rohwedder B, Scully M O, Zubairy M S 2007 Quantum Computing Devices Principles, Designs, and Analysis (1st ed) (Boca Raton: Chapman & Hall/CRC) p347
[19] Duan L M, Kimvle H J 2004 Phys. Rev. Lett. 92 127902
[20] Lin Xiumin 2005 PH.D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [林秀敏 2005 博士学位论文 (合肥:中国科学技术大学)]
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