Jerzy Karczmarczuk
ABSTRACT
We present a framework for representing quantum entities in Haskell. States and operators are functional objects, and their semantics is defined --- as far as possible --- independently of the base in the Hilbert space. We construct effectively the tensor states for composed systems, and we present a toy model of quantum circuit toolbox. We conclude that functional languages are right tools for formal computations in quantum physics. The paper focuses mainly on the representation, not on computational problems.
- D. Deutsch, R. Jozsa, Rapid solution of problems by quantum computer, Proc. Roy. Society, A400, (1992), pp. 553--558.]]Google Scholar
Cross Ref
- 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.]]Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]]Google ScholarCross Ref
- Richard P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, (1982), pp. 467--488.]]Google ScholarCross Ref
- John Preskill, Quantum Information and Computation, Lecture Notes for Physics 229, California Institute of Technology, (1988).]]Google Scholar
- B.M. Boghosian, W. Taylor, Simulating quantum mechanics on a quantum computer, Online preprint quant-ph/9701019, (1997).]]Google Scholar
- D.G. Cory, et al., Quantum Simulations on a Quantum Computer, Phys. Rev. Lett. 82, (1999), pp. 5381-5384.]]Google ScholarCross Ref
- C. Zalka, C. Efficient simulation of quantum systems by quantum computers. Online preprint quant-ph/9603026, (1996).]]Google Scholar
- S. Lloyd, Universal Quantum Simulators, Science 273, (1996), pp. 1073--1078.]]Google ScholarCross Ref
- Shin-Cheng Mu, R. Bird, Functional Quantum Programming, 2nd Asian Workshop on Programming Languages and Systems, KAIST, Dajeaon, Korea, (2001).]]Google Scholar
- Amr Sabry, Modeling Quantum Computing in Haskell, These proceedings: Haskell Workshop, Uppsala, (2003).]] Google ScholarDigital Library
- Bernhard Omer, Procedural Formalism for Quantum Computing, (1998), available from http://tph.tuwien.ac.at/~oemer|.]]Google Scholar
- Paolo Zuliani, Quantum Programming, PhD. thesis, St. Cross College, Univ. of Oxford, (2001).]]Google Scholar
- Julia Wallace, Quantum Computer Simulation - A Review; ver. 2.0, Univ. of Exeter tech. report, (1999), see also the site \verb|www.dcs.ex.ac.uk/~jwallace/simtable.html|, (2002).]]Google Scholar
- X. Wang, A. Sørensen, K. Mølmer, Multibit Gates for Quantum Computing, Phys. Rev. Lett. 86, pp. 3907--3910, (2001).]]Google ScholarCross Ref
- E. Knill, Conventions for Quantum Pseudocode, LANL Rep. LAUR-96-2724.]]Google Scholar
- P.A.M. Dirac, The Principles of Quantum Mechanics, Clarendon press, Oxford, (1958).]]Google Scholar
- Albert Messiah, Quantum Mechanics, Dover Pubs., (2000), or any other, relatively modern book on quantum theory.]]Google Scholar
- G.J. Sussman, J. Wisdom, with M.E. Mayer, Structure and Interpretation of Classical Mechanics, M.I.T Press, (2002).]] Google ScholarDigital Library
- 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).]]Google Scholar
- Daniel Kastler, Introduction à l'électrodynamique quantique, Dunod, Paris, (1960).]]Google Scholar
- Jerzy Karczmarczuk, Scientific Computation and Functional Programming, Computing in Science and Engineering, Vol. 1, (2001), pp. 64-72.]] Google ScholarDigital Library
- Jerzy Karczmarczuk, Generating power of Lazy Semantics, Theor. Comp. Science 187, (1997), pp. 203--219.]] Google ScholarDigital Library
- 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.]]Google Scholar
- John Baez, Web site math.ucr.edu/home/baez/photon/schmoton.htm.]]Google Scholar
- Mark P. Jones, Type Classes with Functional Dependencies, Proc. of the 9-th European Conf. on Programming, ESOP'2000, Springer LNCS 1782, Berlin, (2000).]] Google ScholarDigital Library
- John S. Bell, Speakable and Unspeakable in Quanatum Mechanics, Cambridge Univ. Press, (1989).]]Google Scholar
- Tim Sheard, Simon Peyton Jones, Template meta-programming for Haskell, ACM, Haskell Workshop, Pittsburgh (2002), pp. 1--16.]] Google ScholarDigital Library
- A. Einstein, B. Podolski, N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, (1935), p. 777.]]Google ScholarCross Ref
- W.K. Wootters, W.H. Zurek, A single quantum cannot be cloned, Nature 299, (1982), p. 802.]]Google ScholarCross Ref
- Jan Skibinski, Haskell Simulator of Quantum Computer, web.archive.org/web/ 20010630025035/ www.numeric-quest.com/ haskell/ QuantumComputer.html]]Google Scholar
Index Terms
- Structure and interpretation of quantum mechanics: a functional framework
Recommendations
Introduction to the World of Quantum Computers
ICCI '06: Proceedings of the 2006 5th IEEE International Conference on Cognitive Informatics - Volume 02The world is changing very fast, and so are the ways of communication and computation. This article is about a new communication and information technology based on the principles of the quantum physics. At first we discuss about some fundamental ...
Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states: Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span nonlocal state or sequential application of few-qubit entangling gates are needed to produce ...
Comments