Universality in quantum computation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3142, Issue , 2004, Pages 793-804

  Jeandel, Emmanuel ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; QUANTUM COMPUTERS; QUANTUM ELECTRONICS;

DECISION PROBLEMS; POLYNOMIAL-TIME ALGORITHMS; QUANTUM GATES; REALISABILITY;

POLYNOMIAL APPROXIMATION;

EID: 33847093939     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-27836-8_67     Document Type: Article

References (15)

1. Post, E.: The two-valued iterative systems of mathematical logic. Volume 5 of Annals Mathematical Studies. Princeton University Press (1941)
2. Fredkin, E., Toffoli, T.: Conservative Logic. International Journal of Theoretical Physics 21 (1982) 219-253
3. Lloyd, S.: Almost any quantum logic gate is universal. Physical Review Letters 75 (1995) 346-349
4. Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proceedings of the Royal Society of London, Series A 449 (1995) 669-677
5. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N.H., Shor, P.W., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Physical Review A 52 (1995) 3457-3467
6. Barenco, A.: A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London, Series A 449 (1995) 679-683
7. Kitaev, A., Shen, Vyalyi: Classical and Quantum computation. Volume 47 of Graduate Studies in Mathematics. American Mathematical Society (2003)
8. Shi, Y.: Both Toffoli and Controlled-NOT need little help to do universal quantum computation. Quantum Information and Computation 3 (2003) 84-92
9. Brylinski, J.L., Brylinski, R.: Universal Quantum Gates. In: Mathematics of Quantum Computation. Chapman & Hall (2002)
10. Derksen, H., Jeandel, E., Koiran, P.: Quantum automata and algebraic groups. to appear in Journal of Symbolic Computation (2004)
11. Onishchik, A., Vinberg, E.: Lie groups and algebraic groups. Springer-Verlag, Berlin (1990)
12. Beals, R.: Algorithms for Matrix Groups and the Tits Alternative. Journal of Computer and System Sciences 58 (1999) 260-279
13. Graham, A.: Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited (1981)
14. Babai, L., Beals, R., Rockmore, D.N.: Deciding finiteness for matrix groups in deterministic polynomial time. In: ISSAC' 93, ACM Press (1993) 117-126
15. Mneimné, R., Tes tard, F.: Introduction à la théorie des groupes de Lie classiques. Hermann (1986)