Subscribe

Issue No.02 - February (2009 vol.58)

pp: 238-250

Chuan-Ching Sue , National Cheng Kung University, Tainan

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.161

ABSTRACT

This study develops a quantum switching device with fully nonblocking properties. Although previous studies have also presented quantum-based solutions for the blocking problem, the proposed schemes are characterized by an increased packet loss, a large number of quantum SWAP gates and an increased propagation delay time complexity. The current study overcomes these drawbacks by designing an N \times N fully nonblocking quantum switch, in which the packet payload is passed through quantum SWAP gates while the packet header is passed through quantum control gates designed by applying a modified quantum Karnaugh mapping method. The allocation of quantum SWAP gates to the different layers within the switch is solved using a Perfect Matching in Complete Graph (PMiCG) algorithm with a time complexity of {\rm O}(N!/(2^{N/2}(N/2)!)). A symmetry-based heuristic method is proposed to reduce the time complexity of the search process for all the perfect matching pairs to a time complexity of {\rm O}(N^{2}). The performance of the proposed quantum switch is compared with that of a quantum self-routing packet switch and a quantum switching/quantum merge sorting scheme, respectively, in terms of the hardware complexity, the propagation delay time complexity, the auxiliary qubit complexity, and the packet loss probability.

INDEX TERMS

Fully meshed, quantum computer, nonblocking, SWAP gate, quantum Karnaugh mapping.

CITATION

Chuan-Ching Sue, "An Enhanced Universal N x N Fully Nonblocking Quantum Switch",

*IEEE Transactions on Computers*, vol.58, no. 2, pp. 238-250, February 2009, doi:10.1109/TC.2008.161REFERENCES

- [1] C.L. Wu and T. Feng, “On a Class of Multistage Interconnection Networks,”
IEEE Trans. Computers, vol. 29, no. 8, pp. 694-702, Aug. 1980.- [2] C.L. Wu and T. Feng, “The Universality of the Shuffle-Exchange Network,”
IEEE Trans. Computers, vol. 30, no. 8, pp.324-332, May 1981.- [3] F.K. Hwang, “The Mathematical Theory of Nonblocking Switching Networks,”
Series on Applied Mathematics, vol. 11, World Scientific, 1998.- [4] C. Clos, “A Study of Non-Blocking Switching Networks,”
Bell System Technical J., vol. 32, no. 2, pp. 406-424, Mar. 1953.- [5] D.G. Cantor, “On Nonblocking Switching Networks,”
Networks, vol. 1, pp. 367-377, 1971.- [6] W.-J. Cheng and W.-T. Chen, “A New Self-Routing Permutation Network,”
IEEE Trans. Computers, vol. 45, no. 5, pp. 630-636, May 1996.- [7] C.Y. Lee and A.Y. Oruc, “Design of Efficient and Easily Routable Generalized Connectors,”
IEEE Trans. Comm., pp.646-650, Feb. 1995.- [8] V.E. Benes,
Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, 1965.- [9] C.C. Sue, W.R. Chen, and C.Y. Huang, “Design and Analysis of a Fully Non-Blocking Quantum Switch,”
Proc. IEEE Int'l Conf. Innovative Computing, Information and Control (ICICIC '06), pp. 421-424, Aug. 2006.- [10] M.K. Shukla, R. Ratan, and A.Y. Oruc, “A Quantum Self-Routing Packet Switch,”
Proc. 38th Ann. Conf. Information Sciences and Systems (CISS '04), pp. 484-489, Mar. 2004.- [11] S.T. Cheng and C.Y. Wang, “Quantum Switching and Quantum Merge Sorting,”
IEEE Trans. Circuits and Systems, vol. 53, no. 2, pp. 316-325, Feb. 2006.- [12] I.M. Tsai and S.Y. Kuo, “Digital Switching in the Quantum Domain,”
IEEE Trans. Nanotechnology, vol. 1, no. 3, pp. 154-164, 2002.- [13] C. Moore and M. Nilsson,
Parallel Quantum Computation and Quantum Codes, http://arxiv.org/quant-ph9808027/, Aug. 1998.- [14] P.W. Diaconis and S.P. Holmes, “Matchings and Phylogenetic Trees,”
Proc. Nat'l Academy of Sciences of the USA, vol. 95, pp.14600-14602, Dec. 1998.- [15] J.-S. Lee, Y. Chung, J. Kim, and S. Lee,
A Practical Method of Constructing Quantum Combinational Logic Circuits, http://arxiv.org/quant-ph9911053, 2007.- [16] I.-M. Tsai and S.-Y. Kuo, “Quantum Boolean Circuit Construction and Layout under Locality Constraint,”
Proc. First IEEE Conf. Nanotechnology, pp. 111-116, 2001.- [17] V.V. Shende, A.K. Prasad, I.L. Markov, and J.P. Hayes, “Reversible Logic Circuit Synthesis,”
Proc. IEEE/ACM Int'l Conf. Computer Aided Design (ICCAD '02), pp. 353-360, Nov. 2002.- [18] K. Iwama, Y. Kambayashi, and S. Yamashita, “Transformation Rules for Designing CNOT-Based Quantum Circuits,”
Proc. 39th Design Automation Conf. (DAC '02), pp. 419-425, June 2002.- [19] K.N. Patel, I.L. Markov, and J.P. Hayes,
Efficient Synthesis of Linear Reversible Circuits, http://arXiv.org/quant-ph0302002, 2003.- [20] S.A. Wang, C.Y. Lu, I.M. Tsai, and S.Y. Kuo, “Modified Karnaugh Map for Quantum Boolean Circuit Construction,”
Proc. Third IEEEConf. Nanotechnology (IEEE-NANO '03), vol. 2, pp. 651-654, Aug. 2003.- [21] T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein,
Introduction to Algorithms. MIT Press, 2001. |