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Duality quantum computing

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Abstract

In this article, we make a review on the development of a newly proposed quantum computer, duality computer, or the duality quantum computer and the duality mode of quantum computers. The duality computer is based on the particle-wave duality principle of quantum mechanics. Compared to an ordinary quantum computer, the duality quantum computer is a quantum computer on the move and passing through a multi-slit. It offers more computing operations than is possible with an ordinary quantum computer. The most two distinct operations are: the quantum division operation and the quantum combiner operation. The division operation divides the wave function of a quantum computer into many attenuated, and identical parts. The combiner operation combines the wave functions in different parts into a single part. The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer. The main structure of duality quantum computer and duality mode, the duality mode, their mathematical description and algorithm designs are reviewed.

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References

  1. Long G L. The general quantum interference principle and the duality computer. Communications in Theoretical Physics, 2006, 45(5): 825–844; Also see arXiv:quant-ph/0512120; It was briefly mentioned in an abstract (5111-53) (Tracking No. FN03-FN02-32) submitted to SPIE conference “Fluctuations and Noise in Photonics and Quantum Optics” in 18 Oct 2002

    MathSciNet  Google Scholar 

  2. Arndt M, Nairz O, Vos-Andreae J, et al. Wave-particle duality of C60 molecules. Nature, 1999, 401: 680–682

    Article  Google Scholar 

  3. Liu Y, Long G L. Duality computing in quantum computers. arXiv: 0708.1986, accepted by Communications in Theoretical Physics

  4. Liu Y, Wang C, Long G L. Allowable generalized quantum gates. accepted by Communications in Theoretical Physics

  5. Wang Y Q, Du H K, Dou Y N. Note on generalized quantum gates and quantum operations. International Journal of Theoretical Physics, (in press). Online first with DOI 10.1007/s10773-008-9659-4

  6. Gudder S. Mathematical theory of duality quantum computers. Quantum Information Processing, 2007, 6(1): 37–48

    Article  MATH  MathSciNet  Google Scholar 

  7. Long G L. Mathematical theory of the duality computer in the density matrix formalism. Quantum Information Processing, 2007, 6(1): 49–54

    Article  MATH  MathSciNet  Google Scholar 

  8. Gudder S. Duality quantum computers and quantum operations. International Journal of Theoretical Physics, 2008, 47(1): 268–279. See also http://www.math.du.edu/data/preprints/m0611.pdf

    Article  MATH  MathSciNet  Google Scholar 

  9. Du H K, Wang Y Q, Xu J L. Applications of the generalized Luders theorem. Journal of Mathematical Physics, 2008, 49(1): 013507

    Google Scholar 

  10. Wootters W, Zurek W. A single quantum cannot be cloned. Nature, 1982, 299: 802–803

    Article  Google Scholar 

  11. Deutsch D. Quantum computational networks. Proceedings of the Royal Society London A, 1989, 425: 73–90

    Article  MATH  MathSciNet  Google Scholar 

  12. Barenco A, Bennett C H, Cleve R, et al. Elementary gates for quantum computation. Physical Review A, 1995, 52(5): 3457–3466

    Article  Google Scholar 

  13. Long G L, Zhou Y F, Jin J Q, et al. Density matrix in quantum mechanics and distinctness of ensembles having the same compressed density matrix. Foundations of Physics, 2006, 36(8): 1217–1243

    Article  MATH  MathSciNet  Google Scholar 

  14. Long G L, Liu Y. Search an unsorted database with quantum mechanics. Frontiers of Computer Science in China, 2007, 1(3): 247–271

    Article  Google Scholar 

  15. Grover L. A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on Theory of Computing. ACM New York, 1996: 212–219

  16. Long G L. Grover algorithm with zero theoretical rate. Physical Review A, 2001, 64: 022307

    Google Scholar 

  17. Bruuschweiler R. Novel strategy for database searching in spin Liouville space by NMR ensemble computing. Physical Review Letters, 2000, 85(22): 4815–4818

    Article  Google Scholar 

  18. Xiao L, Long G L. Fetching marked items from an unsorted database in NMR ensemble computing. Physical Review A, 2002, 66(5): 052320

    Google Scholar 

  19. Long G L, Xiao L. Parallel quantum computing in a single ensemble quantum computer. Physical Review A, 2004, 69(6): 052302

    Google Scholar 

  20. Long G L, Xiao L. Experimental realization of a fetching algorithm in a 7-qubit NMR spin Liouville space computer. Journal of Chemical Physics, 2003, 119(16): 8473–8481

    Article  Google Scholar 

  21. Grover L K. Fixed-point quantum search. Physical Review Letters, 2005, 95(15): 150501

    Google Scholar 

  22. Li D F, Li X R, Huang H T, et al. Fixed-point quantum search for different phase shifts. Physics Letters A, 2007, 362(4): 260–264

    Article  MathSciNet  Google Scholar 

  23. Li D F. Quantum fixed-point search algorithm with general phase shifts. Frontiers of Computer Science in China, 2008, 2(2): 138–142

    Article  MATH  Google Scholar 

  24. Wang W Y, Shang B, Wang C, et al. Prime factorization in the duality computer. Communications in Theoretical Physics, 2007, 47(3): 471–473

    Google Scholar 

  25. Qiu D W, Li L Z. An overview of quantum computation models: quantum automata. Frontiers of Computer Science in China, 2008, 2(2): 193–207

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Tsinghua University, Beijing, 100084, China

    Guilu Long & Yang Liu

  2. Tsinghua National Laboratory for Information Science and Technology, Beijing, 100084, China

    Guilu Long & Yang Liu

Authors
  1. Guilu Long
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  2. Yang Liu
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Corresponding author

Correspondence to Guilu Long.

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Long, G., Liu, Y. Duality quantum computing. Front. Comput. Sci. China 2, 167–178 (2008). https://doi.org/10.1007/s11704-008-0021-z

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  • DOI: https://doi.org/10.1007/s11704-008-0021-z

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