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Issue No.06 - June (2009 vol.58)
pp: 728-743
Mingsheng Ying , Tsinghua University, Beijing
Yuan Feng , Tsinghua University, Beijing
ABSTRACT
A classical circuit can be represented by a circuit graph or equivalently by a Boolean expression. The advantage of a circuit graph is that it can help us to obtain an intuitive understanding of the circuit under consideration, whereas the advantage of a Boolean expression is that it is suited to various algebraic manipulations. In the literature, however, quantum circuits are mainly drawn as circuit graphs, and a formal language for quantum circuits that has a function similar to that of Boolean expressions for classical circuits is still missing. Certainly, quantum circuit graphs will become unmanageable when complicated quantum computing problems are encountered, and in particular, when they have to be solved by employing the distributed paradigm where complex quantum communication networks are involved. In this paper, we design an algebraic language for formally specifying quantum circuits in distributed quantum computing. Using this language, quantum circuits can be represented in a convenient and compact way, similar to the way in which we use Boolean expressions in dealing with classical circuits. Moreover, some fundamental algebraic laws for quantum circuits expressed in this language are established. These laws form a basis of rigorously reasoning about distributed quantum computing and quantum communication protocols.
INDEX TERMS
Quantum computing, circuits, distributed systems.
CITATION
Mingsheng Ying, Yuan Feng, "An Algebraic Language for Distributed Quantum Computing", IEEE Transactions on Computers, vol.58, no. 6, pp. 728-743, June 2009, doi:10.1109/TC.2009.13
REFERENCES
[1] C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. Wootters, “Teleporting an Unknown Quantum State via Classical and EPR Channels,” Physical Rev. Letters, vol. 70, pp.1895-1899, 1993.
[2] J.I. Cirac, A.K. Ekert, S.F. Huelga, and C. Macchiavello, “Distributed Quantum Computation over Noisy Channels,” Physical Rev. A, vol. 59, pp. 4249-4254, 1999.
[3] R. Cleve and H. Buhrman, “Substituting Quantum Entanglement for Communication,” Physical Rev. A, vol. 56, pp. 1201-1204, 1997.
[4] D. Collins, N. Linden, and S. Popescu, “Nonlocal Content of Quantum Operations,” Physical Rev. A, vol. 64, no. 3, p.032302, 2001.
[5] E. D'Hondt and P. Panangaden, “The Computational Power of the W and GHZ States,” Quantum Information and Computation, vol. 6, pp. 173-183, 2006.
[6] R.Y. Duan, Y. Feng, and M.S. Ying, “Entanglement is Not Necessary for Perfect Discrimination between Unitary Operations,” Physical Rev. Letters, vol. 98, no. 10, p. 100503, 2007.
[7] J. Eisert, K. Jacobs, P. Papadopoulos, and M.B. Plenio, “Optimal Local Implementation of Nonlocal Quantum Gates,” Physical Rev. A, vol. 62, p. 052317, 2000.
[8] Y. Feng, R.Y. Duan, Z.F. Ji, and M.S. Ying, “Probabilistic Bisimulations for Quantum Processes,” Information and Computation, vol. 205, pp. 1608-1635, 2007.
[9] S.J. Gay and R. Nagarajan, “Communicating Quantum Processes,” Proc. 32nd ACM Symp. Principles of Programming Languages, ACM Press, 2005.
[10] S.J. Gay and R. Nagarajan, “Typechecking Communicating Quantum Processes,” Math. Structures in Computer Science, vol. 16, pp. 375-406, 2006.
[11] D. Gottesman and I.L. Chuang, “Demonstrating the Viability of Universal Quantum Computation Using Teleportation and Single-Qubit Operations,” Nature, vol. 402, pp. 390-393, 1999.
[12] L.K. Grover, Quantum Telecomputation, arXiv:quant-ph/9704012, 1997.
[13] P. Jorrand and M. Lalire, “Toward a Quantum Process Algebra,” Proc. First ACM Conf. Computing Frontiers, ACM Press, 2005.
[14] P. Jorrand and M. Lalire, “From Quantum Physics to Programming Languages: A Process Algebraic Approach,” Unconventional Programming Paradigms, J.-P. Banatre, P. Fradet, J.-L. Giavitto, and O. Michel, eds., pp. 1-16, Springer, 2005.
[15] R. Jozsa and N. Linden, “On the Role of Entanglement in Quantum-Computational Speed-Up,” Proc. Royal Soc. London, Series A—Math., Physical Eng. Sciences, vol. 459, pp. 2011-2032, 2003.
[16] M. Lalire, “Relations among Quantum Processes: Bisimilarity and Congruence,” Math. Structures in Computer Science, vol. 16, pp. 407-428, 2006.
[17] M. Lalire and F. Jorrand, “A Process Algebraic Approach to Concurrent and Distributed Quantum Computation: Operational Semantics,” Proc. Second Int'l Workshop Quantum Programming Languages, P. Selinger, ed., TUCS General Publications 33, Turku Centre for Computer Science, 2004.
[18] N.A. Lynch, Distributed Algorithms. Morgan Kaufmann, 1996.
[19] A. Serafini, S. Mancinians, and S. Bose, “Distributed Quantum Computation via Optical Fibers,” Physical Rev. Letters, vol. 96, 2006.
[20] S. Tani, H. Kobayashi, and K. Matsumoto, Exact Quantum Algorithms for the Leader Election Problem, V. Diekert and B.Duran, eds., pp. 581-592. Springer-Verlag, 2005.
[21] R. van Meter, W.J. Munro, K. Nemoto, and K.M. Itoh, “Arithmetic on a Distributed-Memory Quantum Multicomputer,” ACM J. Emerging Technologies in Computing Systems, vol. 3, no. 17, pp. 1-23, 2008.
[22] R. van Meter, K. Nemoto, and W.J. Munro, “Communication Links for Distributed Quantum Computation,” IEEE Trans. Computers, vol. 56, no. 12, pp. 1643-1653, Dec. 2007.
[23] G.M. Wang and M.S. Ying, “Perfect Many-to-One Teleportation with Stabilizer States,” Physical Rev. A, vol. 77, p. 032324, 2008.
[24] G.M. Wang and M.S. Ying, “Deterministic Distributed Dense Coding with Stabilizer States,” Physical Rev. A, vol. 77, no. 3, p.032306, 2008.
[25] A. Yimsiriwattana and S.J. Lomonaco, Jr., “Generalized GHZ States and Distributed Quantum Computing,” Coding Theory andQuantum Computing, D. Evans, J.J. Holt, C. Jones, K.Klintworth, B. Parshall, O. Pfister, and H.N. Ward, eds., AMS Contemporary Mathematics 381, 2005.
[26] A. Yimsiriwattana and S.J. Lomonaco, Jr., “Distributed Quantum Computing: A Distributed Shor Algorithm,” Quantum Information and Computation II, E. Donkor, A.R. Pirich, and H.E. Brandt, eds., 2004.
[27] M.S. Ying, Y. Feng, R.Y. Duan, and Z.F. Ji, “An Algebra ofQuantum Processes,” ACM Trans. Computational Logic, to be published.
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