Elementary gates for quantum computation
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Barenco, Adriano
a,b,c,d,e,f,g,h
Bennett, Charles H
a,b,c,d,e,f,g,h
Cleve, Richard
a,b,c,d,e,f,g,h
Divincenzo, David P
a,b,c,d,e,f,g,h
Margolus, Norman
a,b,c,d,e,f,g,h
Shor, Peter
a,b,c,d,e,f,g,h
Sleator, Tycho
a,b,c,d,e,f,g,h
Smolin, John A
a,b,c,d,e,f,g,h
Weinfurter, Harald
a,b,c,d,e,f,g,h
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84927318675
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P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, New York, 1958), Chap. 5; for a modern treatment, see A Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993), Chap. 8.6.
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4
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84927318674
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Yves Lecerf, C. R. Acad. Sci. 257, 2597 (1963)
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6
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84927318673
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for a review, see C. H. Bennett and R. Landauer, Sci. Am. X (7), 48 (1985).
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8
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84927318672
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T. Toffoli, in Automata, Languages and Programming, edited by J. W. de Bakker and J. van Leeuwen (Springer, New York, 1980), p. 632; MIT Technical Memo No. MIT/LCS/TM 151, 19XX (unpublished).
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13
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84927318671
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Tycho Sleator and Harald Weinfurter (unpublished).
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17
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84927318667
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Y. Yamamoto, M. Kitegawa, and K. Igeta, in Proceedings of the Third Asia Pacific Physics Conference, edited by Editor(s) (World Scientific, Singapore, 1988);
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24
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84927318666
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A. Berthiaume and G. Brassard, in Proceedings of the Workshop on Physics and Computation, PhysComp '92, edited by Editor(s) (IEEE, City, 1992), pp. 195 199.
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25
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84927318597
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D. Simon, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by Editor(s) (IEEE Computer Society, Los Alamitos, 1994), p. 116.
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26
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84927318595
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E. Bernstein and U. Vazirani, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, edited by Editor(s) (ACM, New York, 1993), pp. 11 20.
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28
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84927318593
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For a review see A. Ekert and R. Jozsa (unpublished); see also J. Brown, New Sci. 133, 1944, 21 (1994).
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39
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84927318588
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D. Coppersmith, IBM Research Report No. RC19642, 1994 (unpublished); R. Cleve (unpublished).
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40
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84927318587
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A. Berthiaume, D. Deutsch, and R. Jozsa, Proceedings of the Workshop on Physics and Computation, PhysComp '94 (IEEE, Los Alamitos, 1994), p. 60.
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43
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84927318577
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Proc. R. Soc. London (to be published).
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Landauer, R.1
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44
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84927318575
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The only nontrivial one bit classical invertible operation is ( beginarray{cc 0 1 1 0 endarray ).
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46
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84927318573
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Richard Cleve, Ph.D. thesis, University of Toronto, 1989 (unpublished), pp. 2 56.
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48
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84927318571
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Corresponding to the definition in Sec. II, the top two wires contain the input bits x1 and x2 and the third wire contains the input y.
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49
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84927318570
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The angle halving of this definition conforms to the usual relation between operations in SO(3) and SU(2). See J. Mathews and R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, Menlo Park, CA, 1970), p. 464 for the use of SO(3) language (rigid body rotations) to describe SU(2) operations.
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50
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84927318569
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These counts take advantage of a different, entirely classical kind of merging. By an inspection of the truth table of the sequences of the three consecutive wedge1 ( σx ) gates that appear in these simulations, we find that they can always be replaced by just two xor gates.
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