Structure and Interpretation of Quantum Mechanics - A Functional Framework

Proceedings of the 2003 ACM SIGPLAN Haskell Workshop

Volumn , Issue , 2003, Pages 50-61

  Karczmarczuk, Jerzy ^a  

^a UNIVERSITÉ DE CAEN   (France)

Author keywords

Dual bases; Haskell; Multi parametric classes; Operators; Quantum gates; Quantum physics; Tensor products; Vector spaces

Indexed keywords

ABSTRACTING; ALGORITHMS; COMPUTER PROGRAMMING LANGUAGES; COMPUTER SCIENCE; COMPUTER SIMULATION; DATA STRUCTURES; MATHEMATICAL MODELS; TENSORS; VECTORS; LOGIC GATES; QUANTUM ELECTRONICS; QUANTUM OPTICS; VECTOR SPACES;

DUAL BASES; HASKELL; MULTI-PARAMETRIC CLASSES; QUANTUM GATES; QUANTUM PHYSICS; TENSOR PRODUCTS; VECTOR PHYSICS;

QUANTUM THEORY; TENSORS;

DUAL BASIS; HASKELL; QUANTUM GATES; QUANTUM PHYSICS; TENSOR PRODUCTS;

EID: 1542433133     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (33)

1. D. Deutsch, R. Jozsa, Rapid solution of problems by quantum computer, Proc. Roy. Society, A400, (1992), pp. 553-558.
2. Peter Shor, Algorithms for quantum computation: discrete logarithms and factoring, Proc. Symp. on Fundamentals of Computer Science, Los Alamitos, IEEE Press, (1994), pp. 124-134.
3. L.K. Grover, Quantum Mechanics Helps In Searching For a Needle in a Haystack, Phys. Rev. Lett. 79, (1997), p. 325. Also: L.K. Grover, A fast quantum mechanical algorithm for database search, Proc. 28th ACM Symp. on Theory of Computation, (1996), p. 212.
4. L.K. Grover, Quantum Mechanics Helps In Searching For a Needle in a Haystack, Phys. Rev. Lett. 79, (1997), p. 325. Also: L.K. Grover, A fast quantum mechanical algorithm for database search, Proc. 28th ACM Symp. on Theory of Computation, (1996), p. 212.
5. D.S. Abrams, S. Lloyd, Quantum algorithm providing and exponential speed increase in finding eigenvectors and eigenvalues, Phys. Rev. Lett. 83, (1999), pp. 5162-5165.
6. Richard P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, (1982), pp. 467-488.
7. John Preskill, Quantum Information and Computation, Lecture Notes for Physics 229, California Institute of Technology, (1988).
8. B.M. Boghosian, W. Taylor, Simulating quantum mechanics on a quantum computer, Online preprint quant-ph/9701019, (1997).
9. D.O. Cory, et al., Quantum Simulations on a Quantum Computer, Phys. Rev. Lett. 82, (1999), pp. 5381-5384.
10. C. Zalka, C. Efficient simulation of quantum systems by quantum computers. Online preprint quant-ph/9603026, (1996).
11. S. Lloyd, Universal Quantum Simulators, Science 273, (1996), pp. 1073-1078.
12. Shin-Cheng Mu, R. Bird, Functional Quantum Programming, 2nd Asian Workshop on Programming Languages and Systems, KAIST, Dajeaon, Korea, (2001).
13. Amr Sabry, Modeling Quantum Computing in Haskell, These proceedings: Haskell Workshop, Uppsala, (2003).
14. Bernhard Ömer, Procedural Formalism for Quantum Computing, (1998), available from http://tph.tuwien.ac.at/~oemer.
15. Paolo Zuliani, Quantum Programming, PhD. thesis, St. Cross College, Univ. of Oxford, (2001).
16. Julia Wallace, Quantum Computer Simulation - A Review; ver. 2.0, Univ. of Exeter tech. report, (1999), see also the site www.dcs.ex.ac.uk/~jwallace/simtable.html, (2002).
17. X. Wang, A. Soørensen, K. Mølmer, Multibit Gates for Quantum Computing, Phys. Rev. Lett. 86, pp. 3907-3910, (2001).
18. E. Knill, Conventions for Quantum Pseudocode, LANL Rep. LAUR-96-2724.
19. P.A.M. Dirac, The Principles of Quantum Mechanics, Clarendon press, Oxford, (1958).
20. Albert Messiah, Quantum Mechanics, Dover Pubs., (2000), or any other, relatively modern book on quantum theory.
21. G.J. Sussman, J. Wisdom, with M.E. Mayer, Structure and Interpretation of Classical Mechanics, M.I.T Press, (2002).
22. T.C. Ralph, W.J. Munro, G.J. Milburn Quantum Computation with Coherent States, Linear Interactions and Superposed Resources, Univ. of Queensland e-print arXiv:quant-ph/0110115, (2001).
23. Daniel Kastler, Introduction àl'électrodynamique quantique, Dunod, Paris, (1960).
24. Jerzy Karczmarczuk, Scientific Computation and Functional Programming, Computing in Science and Engineering, Vol. 1, (2001), pp. 64-72.
25. Jerzy Karczmarczuk, Generating power of Lazy Semantics, Theor. Comp. Science 187, (1997), pp. 203-219.
26. Diederik Aerts, Ingrid Daubechies, Physical justification for using the tensor product to describe two quantum systems as one joint system, Helvetica Physica Acta, 51, (1978), pp. 661-675.
27. John Baez, Web site math.ucr.edu/home/baez/photon/schmoton.htm.
28. Mark P. Jones, Type Classes with Functional Dependencies, Proc. of the 9-th European Conf. on Programming, ESOP'2000, Springer LNCS 1782, Berlin, (2000).
29. John S. Bell, Speakable and Unspeakable in Quanatum Mechanics, Cambridge Univ. Press, (1989).
30. Tim Sheard, Simon Peyton Jones, Template meta-programming for Haskell, ACM, Haskell Workshop, Pittsburgh (2002), pp. 1-16.
31. A. Einstein, B. Podolski, N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, (1935), p. 777.
32. W.K. Wootters, W.H. Zurek, A single quantum cannot be cloned. Nature 299, (1982), p. 802.
33. Jan Skibiński, Haskell Simulator of Quantum Computer, web.archive.org/web/20010630025035/www.numeric-quest.com/haskell/ QuantumComputer.html