99
Bibliography
[1] T. Bartee, Digital Computer Fundamentals, McGraw–Hill Book Company, New York,
pp. 66–151, 1966. 1
[2] G. Casanova, L’algèbre de Boole, Presses Universitaires de France, Paris, 1967. 1
[3] T. Sasao and M. Fujita, Representation of Discrete Functions, Kluwer Academic Publishers,
Boston, 1996. DOI: 10.1007/978-1-4613-1385-4. 1, 4, 6
[4] A. Gaidukov, Algorithm to derive minimum ESOP for 6-variable function, Proc. of the
5th International Workshop on Boolean Problems, Freiberg, pp. 141–148, September 2002.
6, 7
[5] G. Pogosyan, I. Rosenberg, and S. Takada, Building minimum ESOPs through redun-
dancy elimination, Proc. of the 6th International Workshop on Boolean Problems, Freiberg,
pp. 201–206, September 2004. 6
[6] E. Dubrova, D. Miller, and J. Muzio, Upper bound on number of products in AND-
OR-XOR expansions of logic functions, Electronics Letters, vol. 31, pp. 541–542, 1995.
DOI: 10.1049/el:19950377. 7
[7] e GAP group, GAP—a tutorial, https://www.gap-system.org/Manuals/doc/tut
/manual.pdf, 2016. 10
[8] E. Fredkin and T. Toffoli, Conservative logic, International Journal of Physics, vol. 21,
pp. 219–253, 1982. DOI: 10.1007/bf01857727. 10
[9] A. De Vos, Reversible Computing, Wiley, VCH, Weinheim, 2010. DOI:
10.1002/9783527633999. 14, 21, 40, 44, 65
[10] R. Wille and R. Drechsler, Towards a Design Flow for Reversible Logic, Springer, Dor-
drecht, 2010. DOI: 10.1007/978-90-481-9579-4. 10, 56
[11] M. Soeken, R. Wille, O. Keszöcze, M. Miller, and R. Drechsler, Embedding of large
Boolean functions for reversible logic, ACM Journal on Emerging Technologies in Comput-
ing Systems, vol. 12, p. 41, 2015. DOI: 10.1145/2786982. 10
[12] A. De Vos and Y. Van Rentergem, Young subgroups for reversible comput-
ers, Advances in Mathematics of Communications, vol. 2, pp. 183–200, 2008. DOI:
10.3934/amc.2008.2.183. 14, 34, 35, 37, 40
100 BIBLIOGRAPHY
[13] A. Yong, What is ... a Young tableau?, Notices of the AMS, vol. 54, pp. 240–241, 2007. 14
[14] G. Birkhoff, Tres observaciones sobre el algebra lineal, Universidad Nacional de Tucumán:
Revista Matemáticas y Física Teórica, vol. 5, pp. 147–151, 1946. 15
[15] R. Bhatia, Matrix Analysis, Springer, New York, 1997. DOI: 10.1007/978-1-4612-0653-
8. 15
[16] D. de Werra, Path coloring in bipartite graphs, European Journal of Operational Research,
vol. 164, pp. 575–584, 2005. DOI: 10.1016/j.ejor.2003.05.007. 15
[17] C. Peng, G. Bochman, and T. Hall, Quick Birkhoff-von Neumann decomposition algo-
rithm for agile all-photonic network cores, Proc. of the IEEE International Conference on
Communications, Istanbul, pp. 2593–2598, June 2006. DOI: 10.1109/icc.2006.255170.
15
[18] A. De Vos and Y. Van Rentergem, Reversible computing: From mathematical group the-
ory to electronical circuit experiment, Proc. of the Computing Frontiers Conference, Ischia,
pp. 35–44, May 2005. DOI: 10.1145/1062261.1062270. 17
[19] A. Kerber, Representations of Permutation Groups I, Springer Verlag, Berlin, pp. 17–23,
1970. DOI: 10.1007/bfb0067943. 18
[20] G. James and A. Kerber, e representation theory of the symmetric group,
Encyclopedia of Mathematics and its Applications, vol. 16, pp. 15–33, 1981. DOI:
10.1017/cbo9781107340732.005.
[21] A. Jones, A combinatorial approach to the double cosets of the symmetric group with re-
spect to Young subgroups, European Journal of Combinatorics, vol. 17, pp. 647–655, 1996.
DOI: 10.1006/eujc.1996.0056. 18
[22] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge
University Press, Cambridge, 2000. DOI: 10.1017/cbo9780511976667. 21
[23] B. Eastin and S. Flammia, Q-Circuit tutorial,
http://info.phys.unm.edu/Qcircuit/, 2008. 25
[24] A. De Vos and Y. Van Rentergem, Synthesis of reversible logic for nanoelectronic circuits,
International Journal of Circuit eory and Applications, vol. 35, pp. 325–341, 2007. DOI:
10.1002/cta.413. 31, 32, 34
[25] Y. Van Rentergem and A. De Vos, Synthesis and optimization of reversible circuits, Proc.
of the Reed–Muller Workshop, Oslo, pp. 67–75, May 2007. 34
[26] A. De Vos and Y. Van Rentergem, Networks for reversible logic, Proc. of the 8th Interna-
tional Workshop on Boolean Problems, Freiberg, pp. 41–47, September 2008. 34
BIBLIOGRAPHY 101
[27] L. Chen and L. Yu, Decomposition of bipartite and multipartite unitary gates, Physical
Review A, vol. 91, 032308, 2015. DOI: 10.1103/physreva.91.032308. 35, 44
[28] Y. Van Rentergem, Ontwerp van Reversibele Digitale Schakelingen, Universiteit Gent,
Gent, pp. 133–134, 2007. 37
[29] A. De Vos and Y. Van Rentergem, Multiple-valued reversible logic circuits, Journal of
Multiple-Valued Logic and Soft Computing, vol. 15, pp. 489–505, 2009. 39
[30] C. Clos, A study of non-blocking switching networks, Bell Systems Technical Journal,
vol. 32, pp. 406–424, 1953. DOI: 10.1002/j.1538-7305.1953.tb01433.x. 42
[31] F. Hwang, Control algorithms for rearrangeable Clos networks, IEEE Transactions on
Communications, vol. 31, pp. 952–954, 1983. DOI: 10.1109/tcom.1983.1095923. 42
[32] J. Hui, Switching and Traffic eory for Integrated Broadband Networks, Kluwer Academic
Publishers, Boston, pp. 53–138, 1990. DOI: 10.1007/978-1-4615-3264-4.
[33] J. Chao, Z. Jing, and S. Liew, Matching algorithms for three-stage bufferless Clos
network switches, IEEE Communications Magazine, vol. 41, pp. 46–54, 2003. DOI:
10.1109/mcom.2003.1235594. 42
[34] A. Jajszczyk, Nonblocking, repackable, and rearrangeable Clos networks: 50 years of
the theory evolution, IEEE Communications Magazine, vol. 41, pp. 28–33, 2003. DOI:
10.1109/MCOM.2003.1235591. 42
[35] N. Abdessaied, M. Soeken, M. omsen, and R. Drechsler, Upper bounds for reversible
circuits based on Young subgroups, Information Processing Letters, vol. 114, pp. 282–286,
2014. DOI: 10.1016/j.ipl.2014.01.003. 45
[36] M. Soeken, S. Frehse, R. Wille, and R. Drechsler, RevKit: An open source toolkit for
the design of reversible circuits, Proc. of the 3rd International Workshop on Reversible Com-
putation, Gent, pp. 64–76, July 2011. DOI: 10.1007/978-3-642-29517-1_6. 47
[37] M. Soeken, RevKit, msoeken.github.io/revkit.html, 2016. DOI: 10.1007/978-3-
642-29517-1_6. 47
[38] D. Deutsch, Quantum computation, Physics World, vol. 5, no. 6, pp. 57–61, 1992. DOI:
10.1088/2058-7058/5/6/38. 49
[39] D. Deutsch, A. Ekert, and R. Lupacchini, Machines, logic and quantum physics, e
Bulletin of Symbolic Logic, vol. 3, pp. 265–283, 2000. DOI: 10.2307/421056.
[40] A. Galindo and M. Martín-Delgado, Information and computation: Classical and
quantum aspects, Review of Modern Physics, vol. 74, pp. 347–423, 2002. DOI:
10.1103/revmodphys.74.347.
102 BIBLIOGRAPHY
[41] D. Miller, Decision diagram techniques for reversible and quantum circuits, Proc. of the
8th International Workshop on Boolean Problems, Freiberg, pp. 1–15, September 2008.
[42] S. Vandenbrande, R. Van Laer, and A. De Vos, e computational power of the square
root of NOT, Proc. of the 10th International Workshop on Boolean Problems, Freiberg, pp. 257–
262, September 2012. 49
[43] A. De Vos, J. De Beule, and L. Storme, Computing with the square root of NOT, Serdica
Journal of Computing, vol. 3, pp. 359–370, 2009. 51, 52
[44] O. Elgerd, Control Systems eory, McGraw–Hill Book Company, New York, pp. 384–
411, 1967. 52
[45] A. De Vos, R. Van Laer, and S. Vandenbrande, e group of dyadic unitary
matrices, Open Systems and Information Dynamics, vol. 19, 1250003, 2012. DOI:
10.1142/s1230161212500035. 52
[46] W. Castryck, J. Demeyer, A. De Vos, O. Keszöcze, and M. Soeken, Translating between
the roots of the identity in quantum computers, Proc. of the 48th International Symposium
on Multiple-Valued Logic, Linz, pp. 254–259, May 2018. 53
[47] A. De Vos and S. De Baerdemacker, Matrix calculus for classical and quantum circuits,
ACM Journal on Emerging Technologies in Computing Systems, vol. 11, p. 9, 2014. DOI:
10.1145/2669370. 55, 56
[48] Z. Sasanian and D. Miller, Transforming MCT circuits to NCVW circuits, Proc. of the 3rd
International Workshop on Reversible Computation, Gent, pp. 163–174, July 2011. DOI:
10.1007/978-3-642-29517-1_7. 56
[49] P. Selinger, Efficient Clifford CT approximations of single-qubit operators, Quantum
Information and Computation, vol. 15, pp. 159–180, 2015.
[50] M. Amy, D. Maslov, and M. Mosca, Polynomial-time T -depth optimization
of CliffordCT circuits via matroid partitioning, IEEE Transactions on Computer-
Aided Design of Integrated Circuits and Systems, vol. 33, 1486, 2013. DOI:
10.1109/tcad.2014.2341953. 56
[51] A. De Vos and S. De Baerdemacker, Scaling a unitary matrix, Open Systems and Infor-
mation Dynamics, vol. 21, 1450013, 2014. DOI: 10.1142/s1230161214500139. 56, 63,
64
[52] A. De Vos and S. De Baerdemacker, On two subgroups of U(n), useful for quantum
computing, Journal of Physics: Conference Series: Proceedings of the 30th International Collo-
quium on Group-theoretical Methods in Physics, Gent, ( July 2014), vol. 597, 012030, 2015.
DOI: 10.1088/1742-6596/597/1/012030. 56
BIBLIOGRAPHY 103
[53] D. Bouwmeester and A. Zeilinger, e physics of quantum information: Basic concepts,
In: D. Bouwmeester, A. Ekert, and A. Zeilinger, e Physics of Quantum Information,
Springer Verlag, Berlin, pp. 1–14, 2000. DOI: 10.1007/978-3-662-04209-0. 57
[54] A. De Vos and S. De Baerdemacker, e NEGATOR as a basic building block for quan-
tum circuits, Open Systems and Information Dynamics, vol. 20, 1350004, 2013. DOI:
10.1142/s1230161213500042. 59, 62
[55] A. Hurwitz, Ueber die Erzeugung der Invarianten durch Integration, Nachrichten von der
Königliche Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse,
vol. 1897, pp. 71–90, 1897. DOI: 10.1007/978-3-0348-4160-3_38. 59
[56] M. Poźniak, K. Życzkowski, and M. Kuś, Composed ensembles of random unitary ma-
trices, Journal of Physics A: Mathematical and General, vol. 31, pp. 1059–1071, 1998. DOI:
10.1088/0305-4470/31/3/016. 59, 76
[57] R. Jozsa, Quantum algorithms, In: D. Bouwmeester, A. Ekert, and A. Zeilinger, e
Physics of Quantum Information, Springer Verlag, Berlin, pp. 104–126, 2000. 62
[58] M. Idel and M. Wolf, Sinkhorn normal form for unitary matrices, Linear Algebra and its
Applications, vol. 471, pp. 76–84, 2015. DOI: 10.1016/j.laa.2014.12.031. 63, 69
[59] R. Sinkhorn, A relationship between arbitrary positive matrices and doubly stochas-
tic matrices, Annals of Mathematical Statistics, vol. 35, pp. 876–879, 1964. DOI:
10.1214/aoms/1177703591. 64
[60] T. Beth and M. Rötteler, Quantum algorithms: Applicable algebra and quantum physics,
In: G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H.
Weinfurter, R. Werner, and A. Zeilinger, Quantum Information, Springer Verlag, Berlin,
pp. 96–150, 2001. DOI: 10.1007/3-540-44678-8. 65
[61] A. De Vos and S. De Baerdemacker, e synthesis of a quantum circuit, In: B. Stein-
bach, Problems and New Solutions in the Boolean Domain, Cambridge Scholars Publishing,
pp. 357–368, 2016. 69
[62] H. Führ and Z. Rzeszotnik, On biunimodular vectors for unitary matrices, Linear Algebra
and its Applications, vol. 484, pp. 86–129, 2015. DOI: 10.1016/j.laa.2015.06.019. 70, 74
[63] A. De Vos and S. De Baerdemacker, Block-ZXZ synthesis of an arbitrary quantum cir-
cuit, Physical Review A, vol. 94, 052317, 2016. DOI: 10.1103/physreva.94.052317. 73,
74
[64] N. Higham, Computing the polar decomposition with applications, SIAM Journal on
Scientific and Statistical Computing, vol. 7, pp. 1160–1174, 1986. DOI: 10.1137/0907079.
75, 97
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