Extending graphical representations for compact closed categories with applications to symbolic quantum computation

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

Volumn 5144 LNAI, Issue , 2008, Pages 77-92

  Dixon, Lucas ^a   Duncan, Ross ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Categorical logic; Graph rewriting; Graphical calculi; Interactive theorem proving; Quantum computing

Indexed keywords

CATEGORICAL LOGIC; GRAPH REWRITING; GRAPHICAL CALCULI; INTERACTIVE THEOREM PROVING; QUANTUM COMPUTING;

ADMINISTRATIVE DATA PROCESSING; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL LINGUISTICS; COMPUTER NETWORKS; GRAPHIC METHODS; INFORMATION MANAGEMENT; INFORMATION THEORY; KNOWLEDGE MANAGEMENT; MANAGEMENT INFORMATION SYSTEMS; POWDERS; QUANTUM COMPUTERS; QUANTUM THEORY;

GRAPH THEORY;

EID: 51049105078     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85110-3_8     Document Type: Conference Paper

References (18)

1. Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: LICS 2004, pp. 415-425. IEEE Computer Society, Los Alamitos (2004)
2. Asperti, A., Longo, G.: Categories, Types and Structures. MIT Press, Cambridge (1991)
3. Coecke, B.: Kindergarten quantum mechanics. Lecture Notes (2005)
4. Coecke, B., Duncan, R.: Interacting quantum observables. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS. vol. 5126. pp. 298-310. Springer, Heidelberg (2008)
5. Coecke, B., Paquette, E.O.: POVMs and Naimark's theorem without sums. In: Proc. of the 4th International Workshop on Quantum Programming Languages (2006)
6. Coecke, B., Pavlovic, D.: Quantum measurements without sums. In: The Mathematics of Quantum Computation and Technology. CRC Applied Mathematics & Nonlinear Science. Taylor and Francis (2007)
7. Corradini, A., Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A.: Algebraic approaches to graph transformation - part I: Single pushout approach and comparison with double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. I, pp. 247-312. World Scientific, Singapore (1997)
8. Duncan, R.: Types for Quantum Computation. PhD thesis, Oxford University (2006)
9. Janssens, D., Rozenberg, G.: Graph grammars with node-label controlled rewriting and embedding. In: Proc. of the 2nd International Workshop on Graph-Grammars and Their Application to Computer Science, pp. 186-205. Springer, Heidelberg (1983)
10. Kelly, G.M., Laplaza, M.L.: Coherence for compact closed categories. Journal of Pure and Applied Algebra 19, 193-213 (1980)
11. Pati, A.K., Braunstein, S.L.: Impossibility of deleting an unknown quantum state. Nature 404, 164-165 (2000)
12. Paulson, L.C: Isabelle: A generic theorem prover. Springer, Heidelberg (1994)
13. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188-5191 (2001)
14. Schfürr, A.: Programmed graph replacement systems, pp. 479-546. World Scientific Publishing Co, River Edge (1997)
15. Selinger, P.: Dagger compact closed categories and completely positive maps. In: Proc. of the 3rd International Workshop on Quantum Programming Languages (2005)
16. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J.Sci.Statist.Comput. 26(5) (1997)
17. Velasco, P.P.P., de Lara, J.: Matrix approach to graph transformation: Matching and sequences. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 122-137. Springer, Heidelberg (2006)
18. Wootters, W., Zurek, W.: A single quantum cannot be cloned, Nature 299, 802-803 (1982)