Coupling of quantum angular momenta: An insight into analogic/discrete and local/global models of computation

Natural Computing

Volumn 6, Issue 2, 2007, Pages 151-168

  Marzuoli, Annalisa ^a   Rasetti, Mario ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Analogic and discrete models of computation; Binary coupling of quantum angular momenta; Quantum automata; Quantum complexity theory; Racah Wigneralgebra; SU (2) recoupling theory; Topological quantum computation

Indexed keywords

ALGORITHM; ARTICLE; COMPUTER ANALYSIS; COMPUTER LANGUAGE; COMPUTER SIMULATION; COMPUTER SYSTEM; CORRELATION ANALYSIS; INFORMATION PROCESSING; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; MATHEMATICS; QUANTUM THEORY;

EID: 34250208461     PISSN: 15677818     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11047-006-9018-4     Document Type: Article

References (20)

1. Biedenharn LC and Louck JD (1981) The Racah-Wigner algebra in quantum theory, Encyclopedia of Mathematics and its Applications vol 9, Rota GC Editor, Addison-Wesley, Reading, MA. Topic 9: Physical interpretation and asymptotic limits of the angular momentum functions; Topic 12: Coupling of N angular momenta, recoupling theory.
2. Birman JS aAd Brendle TE (2004) Braids: A survey, arXiv:math./GT/040905
3. Churchland PS, Sejnowski TJ (1992). The Computational Brain. the MIT Press, Cambridge, MA
4. Feynman RP (1982). Simulating physics with computers. International Journal of Theoretical Physics 21:467-488
5. Feynman RP (1996) Feynman Lectures on Computation, Hey AJG and Allen RW (eds), Penguin Group, London, p. xiv
6. Freedman MH (1998). P/NP, and the quantum field computer. Proc. National Academy of Sciences USA (Computer Science) 95:98-101
7. Freedman MH, Kitaev A, Larsen MJ, Wang Z (2002). Topological quantum computation. Bulletin of the American Mathematical Society 40:31-38
8. Garey MR and Johnson DS (1979) Computers and intractability, a guide to the theory of NP-completeness, Freeman and Co., New York
9. Garnerone S, Marzuoli A and Rasetti M (2006a) Spin networks, quantum automata and link invariants. Journal of Physics: Conference Series 33: 95-106
10. Garnerone S, Marzuoli A and Rasetti M (2006) Quantum automata, braid group and link polynomials, arXiv:qUant-ph/0601169
11. Jaeger F, Vertigan DL, Welsh DJA (1990). Mathematical proceedings of the Cambridge. Philosophical Society 108:35-53
12. Jones V (1987) Hecke algebra representations of braid groups and link polynomials. Annals of Mathematics: 335-388
13. Marzuoli A, Rasetti M (2002) Spin network quantum simulator. Physics Letters A 306:79-87
14. Marzuoli A, Rasetti M (2005a). Computing spin networks. Annals of Physics 318:345-407
15. Marzuoli A, Rasetti M (2005b). Spin network setting of topological quantum computation. International Journal of Quantum Information 3:65-72
16. Ponzano G and Regge T (1968) Semiclassical limit of Racah coefficients. In: Bloch F et al. (eds), Spectroscopic and Group Theoretical Methods in Physics, Editors, North-Holland, Amsterdam, pp. 1-58
17. Turaev V, Viro OY (1992). State sum invariants of 3-manifolds and quantum 6 j symbols. Topology 31:865-902
18. Varshalovich DA, Moskalev AN and Khersonskii VK (1988) Quantum Theory of Angular Momentum, World Scientific, Singapore
19. von Neumann J (1951) The general and logical theory of automata, The Hixon Symposium, Wiley, New York; reprinted in John von Neumann Collected Works, Vol. V (1963), Pergamon, Oxford, pp. 288-328
20. Witten E (1989). Quantum field theory and the Jones polynomial. Communications in Mathematical Physics 121:351-399