Linear-algebraic λ-calculus: Higher-order, encodings, and confluence

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

Volumn 5117 LNCS, Issue , 2008, Pages 17-31

  Arrighi, Pablo ^a   Dowek, Gilles ^b  

^a UNIV GRENOBLE ALPES   (France)

^b ÉCOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL MECHANICS; DIFFERENTIATION (CALCULUS); LINEAR ALGEBRA; MATHEMATICAL OPERATORS; QUANTUM COMPUTERS;

ENCODINGS; HIGHER-ORDER; LAMBDA CALCULUS; LINEAR COMBINATIONS; LINEAR OPERATORS; LINEAR-ALGEBRAIC; MINIMAL LANGUAGES; REWRITE RULES;

CALCULATIONS;

EID: 48949095462     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-70590-1_2     Document Type: Conference Paper

References (30)

1. Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols LICS. IEEE Computer Society, 415-425 (2004)
2. Altenkirch, T., Grattage, J., Vizzotto, J.K., Sabry, A.: An Algebra of Pure Quantum Programming. In: Third International Workshop on Quantum Programming Languages. Electronic Notes of Theoretical Computer Science, vol. 170C, pp. 23-47 (2007)
3. Arrighi, P., Dowek, G.: A computational definition of the notion of vectorial space. ENTCS 117, 249-261 (2005)
4. Arrighi, P., Dowek, G.: Linear-algebraic lambda-calculus. In: Selinger, P. (ed.) International workshop on quantum programming languages, Turku Centre for Computer Science General Publication, vol. 33, pp. 21-38 (2004)
5. Arrighi, P., Dowek, G.: Linear-algebraic lambda-calculus: higher-order, encodings, confluence, arXiv:quant-ph/0612199.
6. Bernstein, E., Vazirani, U.: Quantum Complexity Theory. In: Annual ACM symposium on Theory of Computing, vol. 25 (1993)
7. Boudol, G.: Lambda-calculi for (strict) parallel functions. Information and Computation 108(1), 51-127 (1994)
8. Bournez, O., Hoyrup, M.: Rewriting Logic and Probabilities. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706. Springer, Heidelberg (2003)
9. Boykin, P., Mor, T., Pulver, M., Roychowdhury, V., Vatan, F.: On universal and fault-taulerant quantum computing, arxiv:quant-ph/9906054
10. http://cime.lri.fr/
11. Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Handbook of theoretical computer science. formal models and semantics, vol. B. MIT press, Cambridge (1991)
12. Deutsch, D., Josza, R.: Rapid solution of problems by quantum computation. Proc. of the Roy. Soc. of London A 439, 553-558 (1992)
13. Dougherty, D.: Adding Algebraic Rewriting to the Untyped Lambda Calculus. In: Proc. of the Fourth International Conference on Rewriting Techniques and Applications (1992)
14. Ehrhard, T., Regnier, L.: The differential lambda-calculus. Theoretical Computer Science 309, 1-41 (2003)
15. Di Pierro, A., Hankin, C., Wiklicky, H.: Probabilistic λ-calculus and quantitative program analysis. J. of Logic and Computation 15(2), 159-179 (2005)
16. Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1-102 (1987)
17. Grover, L.K.: Quantum Mechanics Helps in Searching for a Needle in a Haystack. Phys. Rev. Lett. 79(2), 325-328 (1997)
18. Herescu, O.M., Palamidessi, C.: Probabilistic asynchronous pi-calculus. In: Tiuryn, J. (ed.) ETAPS 2000 and FOSSACS 2000. LNCS, vol. 1784, pp. 146-160. Springer, Heidelberg (2000)
19. Jouannaud, J.-P., Kirchner, H.: Completion of a Set of Rules Modulo a Set of Equations. SIAM J. of Computing 15(14), 1155-1194
20. Newman, M.H.A.: On theories with a combinatorial definition of "equivalence". Annals of Mathematics 432, 223-243 (1942)
21. Nielsen, M.A.: Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state. Phys. Rev. A 308, 96-100 (2003)
22. Peterson, G.E., Stickel, M.E.: Complete Sets of Reductions for Some Equational Theories. J. ACM 28(2), 233-264 (1981)
23. Perdrix, S.: State transfer instead of teleportation in measurement-based quantum computation. Int. J. of Quantum Information 1(1), 219-223 (2005)
24. Raussendorf, R., Browne, D.E., Briegel, H.J.: The one-way quantum computer - a non-network model of quantum computation. Journal of Modern Optics 49, 1299 (2002)
25. Selinger, P.: Towards a quantum programming language. Math. Struc. in Computer Science 14(4), 527-586 (2004)
26. Selinger, P., Valiron, B.: A lambda calculus for quantum computation with classical control. Math. Struc. in Computer Science 16(3), 527-552 (2006)
27. Shor, P.W.: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. on Computing 26, 1484-1509 (1997)
28. Van Tonder, A.: A Lambda Calculus for Quantum Computation, arXiv:quant-ph/0307150 (July 2003)
29. Vaux, L.: On linear combinations of lambda-terms. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 374-388. Springer, Heidelberg (2007)
30. Wooters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802-803 (1982)