This Article 
 Bibliographic References 
 Add to: 
An Enhanced Universal N x N Fully Nonblocking Quantum Switch
February 2009 (vol. 58 no. 2)
pp. 238-250
Chuan-Ching Sue, National Cheng Kung University, Tainan
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.

[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,, 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,, 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,, 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.

Index Terms:
Fully meshed, quantum computer, nonblocking, SWAP gate, quantum Karnaugh mapping.
Chuan-Ching Sue, "An Enhanced Universal N x N Fully Nonblocking Quantum Switch," IEEE Transactions on Computers, vol. 58, no. 2, pp. 238-250, Feb. 2009, doi:10.1109/TC.2008.161
Usage of this product signifies your acceptance of the Terms of Use.