Quantum circuit oracles for Abstract Machine computations

Theoretical Computer Science

Volumn 411, Issue 11-13, 2010, Pages 1501-1520

  Hines, Peter ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Abstract Machines; Circuit model; Conditional iteration; Quantum computing

Indexed keywords

ABSTRACT MACHINES; ANCILLA; CIRCUIT MODELS; GARBAGE COLLECTION; GENERAL MODEL; QUANTUM CIRCUIT; QUANTUM COMPUTING; REVERSIBLE COMPUTATIONS; WORST-CASE PERFORMANCE;

CIRCUIT THEORY; LOGIC CIRCUITS; QUANTUM COMPUTERS; QUANTUM OPTICS; QUANTUM THEORY; REFUSE COLLECTION; WASTE DISPOSAL;

ABSTRACTING;

EID: 76449120591     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2009.11.017     Document Type: Article

References (44)

1. Abramsky S., and Jagadeesan R. Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic 59 (1994) 543-574
2. Abramsky S. Retracing some paths in Process algebra. CONCUR 96, Lecture Notes in Computer Science (1996), Springer-Verlag 1-17
3. Abramsky S., and Coecke B. A categorical semantics of quantum protocols. Proc. 19th Annual IEEE Symp. on Logic in Computer Science. LICS 2004 (2005), IEEE Computer Soc. Press 415-425
4. Abramsky S. Abstract scalars, loops, and free traced and strongly compact closed categories. Proceedings of CALCO 2005. LNCS 3629 (2005), Springer 1-31
5. Abramsky S., Haghverdi E., and Scott P. Geometry of interaction and linear combinatory algebras. Mathematical Structures in Computer Science 12 5 (2002)
6. Barr M. Algebraically compact functors. Journal of Pure and Applied Algebra 82 (1992) 211-231
7. Bennett C. Logical reversibility of computation. IBM Journal of Research and Development 17 (1979)
8. Bennett C. Time-space trade-offs for reversible computation. SIAM Journal on Computing 18 (1989) 766
9. Bernstein E., and Vazirani U. Quantum complexity theory. SIAM Journal on Computing 26 5 (1997) 1411-1473
10. Blass A. A game semantics for linear logic. Annals of Pure and Applied Logic 56 (1992) 151-166
11. V. Danos, L. Regnier, Local and asynchronous β-reduction, in: Proceedings of the Eighth Annual IEEE Symp. on Logic in Computer Science, 1993
12. Deutsch D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London, A 400 (1985) 97-117
13. T. Draper, Addition on a Quantum Computer, arXiv:quant-ph/0008033v1, 2000
14. Girard J.-Y. Geometry of Interaction I, Proceedings Logic Colloquium '88 (1988), North-Holland p. 221-260
15. E. Haghverdi, A categorical approach to linear logic, geometry of proofs and full completeness, Ph.D. Thesis, U. of Ottawa, 2000
16. Haghverdi E., and Scott P. A categorical model for the geometry of interaction. Automata, Languages and Programming: Proc. 31st International Colloquium. LNCS vol. 2004 (2004), Springer Journal version: [17]
17. Haghveri E., and Scott P. A categorical model for the geometry of interaction. Theoretical Computer Science 350 2 (2006) 252-274
18. E. Haghveri, P. Scott, Geometry of interaction and the dynamics of proof reduction: A tutorial, in New Structures for Physics, in: Springer Lecture Notes in Physics Series (in press)
19. Hasegawa M. On traced monoidal closed categories. Mathematical Structures in Computer Science 19 2 (2009) 217-244
20. P. Hines, The algebra of self-similarity and its applications, Ph.D. Thesis, U. of Wales, Bangor, 1998
21. Hines P. Physical systems as constructive logics. In: Calude C., Dinneen M., Paun G., Rozenberg G., and Stepney S. (Eds). Unconventional Computation, UC 2006: York, UK. LNCS (2006), Springer
22. Hines P. Machine Semantics - from causality to computational models. International Journal of Unconventional Computation 4 3 (2008) 249-272
23. Hines P. Machine semantics. Theoretical Computer Science 409 (2008) 1-23
24. Hines P., and Braunstein S. The structure of partial isometries. In: Gay S., and Mackie I. (Eds). Semantic Techniques in Quantum Computation (2009), Cambridge University Press 361-388
25. P. Hines, P. Scott, Categorical traces from single-photon linear optics (submitted for publication) available as http://www.peterhines.net/downloads/papers/optics.pdf
26. P. Hines, From termination to cyclic behaviour: Machine semantics and period-finding, Drafts available from: http://www.peterhines.net/downloads/drafts/cyclic-termination/(in preparation)
27. Joyal A., Street R., and Verity D. Traced monoidal categories. Mathematical Proceedings of the Cambridge Philosophical Society (1996) 425-446
28. Kelly G., and Laplaza M. Coherence for compact closed categories. Journal of Pure and Applied Algebra 19 (1980) 193-213
29. Kieu T., and Danos M. A No-Go theorem for halting a universal quantum computer. Acta Physica Hungarica A 14 1 (2001) 217-225
30. Lawson M.V. Inverse Semigroups (1998), World Scientific, Singapore
31. n où θ est un isomorphism de codes. Comptes Rendus 257 (1963) 2579-2600
32. Levine R., and Sherman A. A note on Bennett's time-space trade-off for reversible computation. SIAM Journal on Computing 19 4 (1990) 673-677
33. Li M., and Vitanyi P. Reversible simulation of irreversible computation. Proceedings of the 11th IEEE Conference on Computational Complexity (1996) 301-306
34. N. Linden, S. Popsecue, The halting problem for quantum computers, arXiv:quant-ph/9806054v2, 1998
35. C. Lutz, JANUS-a time-reversible language. Letter to Landauer, available as: http://www.cise.ufl.edu/~mpf/rc/janus.html, 1986
36. Manes E., and Arbib M. Algebraic Approaches to Program Semantics (1986), Springer-Verlag
37. van Meter R., and Itoh K. Fast quantum modular exponentiation. Physical Review A 71 (2005)
38. T. Miyadera, M. Ohya, Designing quantum turing machine is uncomputable, in: Proc. EQIS02, 2002
39. Miyadera T., and Ohya M. On halting process of quantum turing machine. Open Systems and Information Dynamics 12 3 (2005) 261-265
40. Myers J. Can a universal computer be fully quantum?. Physical Review Letters 78 9 (1997) 1823-1824
41. Nielsen M., and Chuang I. Quantum Computation and Quantum Information (2000), Cambridge University Press
42. Selinger P. Towards a quantum programming language. Mathematical Structures in Computer Science 14 4 (2004) 527-586
43. Shor P. Polynomial-time algorithms for prime factorisation and discrete logarithms on a quantum computer. SIAM Review 41 (1999) 303-332
44. V. Vedral, M. Plenio, Basics of quantum computation, arXiv:quant-ph/9802065v1, 1998