Circuits for m-valued classical, reversible and quantum optical computing with application to regular logic design

International Journal of Intelligent Computing and Cybernetics

Volumn 2, Issue 1, 2009, Pages 52-101

  Al Rabadi, Anas N ^a,b  

^a UNIVERSITY OF JORDAN   (Jordan)

^b PORTLAND STATE UNIVERSITY   (United States)

Author keywords

Circuits; Decision trees; Logic; Special purpose computers

Indexed keywords

BASIC BUILDING BLOCK; BASIC LOGIC; CIRCUITS; COHERENT LIGHT BEAMS; DESIGN/METHODOLOGY/APPROACH; FUTURE TECHNOLOGIES; GRAPH-BASED; INCIDENT ANGLES; LIGHT-MATTER INTERACTIONS; LINEAR OPTICAL; LINEAR OPTICAL DEVICES; LOGIC; LOGIC SYNTHESIS; MANAKOV SOLITONS; OPTICAL CIRCUITS AND SYSTEM; OPTICAL COMPUTING; OPTICAL PROCESSING; OPTICAL REALIZATION; OPTIMAL DESIGN; POWER CONSUMPTION; QUANTUM COMPUTING; QUANTUM DECISION TREES; QUANTUM OPTICAL SYSTEMS; REVERSIBLE CIRCUITS; REVERSIBLE LOGIC; SPECIAL PURPOSE COMPUTERS; SUPER-HIGH SPEED; SYSTOLIC ARCHITECTURE;

COMPUTER CIRCUITS; COMPUTER SCIENCE; DECISION TREES; ELECTRIC POWER SUPPLIES TO APPARATUS; GRAPH THEORY; INTEGRATED OPTOELECTRONICS; LIGHT TRANSMISSION; LOGIC DESIGN; LOGIC GATES; MULTIPLEXING; MULTIPLEXING EQUIPMENT; OPTICAL DATA PROCESSING; OPTICAL FILTERS; OPTICAL INSTRUMENTS; OPTICAL PROPERTIES; PHOTONS; QUANTUM COMPUTERS; QUANTUM OPTICS; QUANTUM THEORY; SOLITONS; SPIN DYNAMICS; SWITCHES; SWITCHING CIRCUITS; SYNTHESIS (CHEMICAL);

LOGIC CIRCUITS;

EID: 73849133240     PISSN: 1756378X     EISSN: 17563798     Source Type: Journal    
DOI: 10.1108/17563780910939255     Document Type: Article

References (73)

1. Ablowitz, M.J. and Clarkson, P.A. (1991), Solitons, Nonlinear Evolution Equations, and Inverse Scattering, Cambridge University Press, Cambridge.
2. Ablowitz, M.J., Keiser, J.M. and Takhtajan, L.A. (1991), Class of stable multisate time-reversible cellular automata with rich particle content, Phys. Rev. A, Vol. 44A No. 10, pp. 6909-12.
3. Al-Rabadi, A.N. (2004), Reversible Logic Synthesis: From Fundamentals to Quantum Computing, Springer, New York, NY.
4. Al-Rabadi, A.N. (2005a), Three-dimensional lattice logic circuits, Part I: fundamentals, Facta Universitatis, Vol. 18 No. 1, pp. 1-13.
5. Al-Rabadi, A.N. (2005b), Three-dimensional lattice logic circuits, Part II: formal methods, Facta Universitatis, Vol. 18 No. 1, pp. 15-28.
6. Al-Rabadi, A.N. (2005c), Three-dimensional lattice logic circuits, Part III: solving 3D volume congestion problem, Facta Universitatis, Vol. 18 No. 1, pp. 29-43.
7. Al-Rabadi, A.N. (2007a), Reversible systolic arrays, Part I: two-valued bijective single-instruction multiple-data (SIMD) architectures and their quantum extensions, Proceedings of the International Workshop on Spectral Methods and Multirate Signal Processing (SMMSP), Paper No. 1, pp. 1-12.
8. Al-Rabadi, A.N. (2007b), Reversible systolic arrays, Part II: m-ary equipollent SIMD circuits and their quantum realizations, Proceedings of the International Workshop on Spectral Methods and Multirate Signal Processing (SMMSP), Paper No. 2, pp. 1-11.
9. Al-Rabadi, A.N. and Casperson, L.W. (2002), Optical realizations of reversible logic, Proceedings International Workshop on Logic and Synthesis (IWLS), pp. 21-6.
10. Bell Labs (1998), Micro-mirrors and free-space optics used to route optical signals, Technical Report, Bell Labs, Murray Hill, NJ.
11. Bennett, C. (1973), Logical reversibility of computation, IBM Journal of Research and Development, Vol. 17, pp. 525-32.
12. Bourbaki, N. (1988), Algebra, Springer, New York, NY.
13. Brenner, K.-H. and Huang, A. (1986), Logic and architectures for digital optical computers, J. Opt. Soc. Am. A., Vol. 3, p. 62.
14. Cirac, J.I. and Zoller, P. (1995), Quantum computations with cold trapped ions, Phys. Rev. Let., Vol. 74 No. 20, pp. 4091-4.
15. Cuykendall, R. and Andersen, D.R. (1987), Reversible computing: all-optical implementation of interaction and Priese Gates, Optics Communications, Vol. 62 No. 4, pp. 232-6.
16. Cuykendall, R. and McMillin, D. (1987), Control-specific optical Fredkin circuits, Applied Optics, Vol. 26 No. 10, pp. 1959-63.
17. Dirac, P. (1930), The Principles of Quantum Mechanics, 1st ed., Oxford University Press, Oxford.
18. Dragoman, D. (2002), n-Step optical simulation of the n-qubit state: applications in optical computing, Optik - International J. for Light and Electron Optics, Vol. 113 No. 10, pp. 425-8.
19. Drazin, P.G. and Johnson, R.S. (1989), Solitons: An Introduction, Cambridge University Press, Cambridge.
20. Feynman, R. (1996), Feynman Lectures on Computation, Addison Wesley, Reading, MA.
21. Fokas, A.S., Papadopoulou, E. and Saridakis, Y. (1989), Particles in soliton cellular automata, Complex Systems, Vol. 3, pp. 615-33.
22. Fredkin, E. and Toffoli, T. (1982), Conservative logic, Int. Journal of Theoretical Physics, Vol. 21, pp. 219-53.
23. Goswami, D. (2005), Adiabatic quantum computing with phase modulated laser pulses, Journal of Physics A: Mathematical and General, Vol. 38 No. 38, pp. L615-26.
24. Goswami, D. (2007), On the practicality of adiabatic quantum computing with optical schemes, Int. J. Quantum Information, Vol. 5 Nos 1/2, pp. 179-88.
25. Gray, R. and Casperson, L.W. (1978), Optooptic modulation based on gain saturation, IEEE J. of Quantum Electronics, Vol. QE-14 No. 11.
26. Griffiths, D.J. (1987), Introduction to Elementary Particles, Wiley, New York, NY.
27. Haist, T. and Osten, W. (2009), Ultrafast digital-optical arithmetic using wave-optical computing, International Workshop on Optical Super Computing, pp. 25-50.
28. Hecht, E. (2002), Optics, Addison-Wesley, Reading, MA.
29. Jakubowski, M.H. (1998), Computing with solitons in bulk media, PhD dissertation, Princeton University, Princeton, NJ.
30. Jakubowski, M.H., Steiglitz, K. and Squier, R.K. (1996), When can solitons compute?, Complex Systems, Vol. 10 No. 1, pp. 1-21.
31. Jakubowski, M.H., Steiglitz, K. and Squier, R. (1998), State transformations of colliding optical solitons and possible application to computation in bulk media, Physical Review E, Vol. 58, pp. 6752-8.
32. Jakubowski, M.H., Steiglitz, K. and Squier, R. (2001), Computing with solitons: a review and prospectus, J. of Multiple-valued Logic, Vol. 6 Nos 5/6, special issue on collision-based computing, pp. 439-62.
33. Kang, J.U., Stegeman, G.I., Aitchison, J.S. and Akhmediev, N.N. (1996), Observation of Manakov spatial solitons in AlGaAs planar waveguides, Physical Review Letters, Vol. 76, pp. 3699-702.
34. Kung, H.T. (1982), Why systolic architectures?, Computer, Vol. 15 No. 1, pp. 37-46.
35. Kung, H.T., Wang, C-C., Huang, C-J. and Tsai, K-C. (2000), A 1.00 GHz 0.6-(m 8-bit carry lookahead adder using PLA-styled all-n-transistor logic, IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 47, pp. 133-5.
36. Kung, S.Y. (1988), VLSI Array Processors, Prentice-Hall, Englewood Cliffs, NJ.
37. Landauer, R. (1961), Irreversibility and heat generation in the computational process, IBM Journal of Research and Development, Vol. 5, pp. 183-91.
38. Lounesto, P. (2001), Clifford Algebras and Spinors, Cambridge University Press, Cambridge.
39. Makhankov, V.G. (1990), Soliton Phenomenology, Kluwer Academic Publishers, Norwell, MA.
40. Manakov, S.V. (1974), On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Soviet Physics: JETP, Vol. 38 No. 2, pp. 248-53.
41. Mano, M.M. and Kime, C.R. (2008), Logic and Computer Design Fundamentals, 4th ed., Prentice-Hall, Englewood Cliffs, NJ.
42. Margolus, N. (1984), Physics-like models of computation, Physica, Vol. 10D, pp. 81-95.
43. Marino, A. and Stroud, C.R. (2008), Phase-locked laser system for use in atomic coherence experiments, Review of Scientific Instruments, Vol. 79, p. 013104.
44. Mihai, O. (2006), A light-based device for solving the hamiltonian path problem, Unconventional Computing Conference, Vol. LNCS 4135, pp. 217-27.
45. Muthukrishnan, A. and Stroud, C.R. (2000), Multivalued logic gates for quantum computation, Physical Review A, Vol. 62, p. 052309.
46. Myrick, M.L. and Haibach, F.G. (2004), Precision in multivariate optical computing, Applied Optics, Vol. 43 No. 10, pp. 2130-40.
47. Nielsen, M. and Chuang, I.L. (2000), Quantum Computation and Quantum Information, Cambridge University Press, Cambridge.
48. Park, J.K., Steiglitz, K. and Thurston, W.P. (1986), Soliton-like behavior in automata, Physica D, Vol. 19D, pp. 423-32.
49. Parks, T.W. and Burrus, C.S. (1987), Digital Filter Design, Wiley, New York, NY.
50. Radhakrishnan, R., Lakshmanan, M. and Hietarinta, J. (1997), Inelastic collision and switching of coupled bright solitons in optical fibers, Physical Review E, Vol. 56, pp. 2213-6.
51. Ralph, T.C., Resch, K.J. and Gilchrist, A. (2007), Efficient Toffoli gates using qudits, Phys. Rev. A, Vol. 75, p. 022313.
52. Rebbi, C. and Soliani, G. (1984), Solitons and Particles, World Scientific, Singapore.
53. Reddy, S.M. (1972), Easily testable realizations of logic functions, IEEE Trans. Comp., Vol. C-21, pp. 1183-8.
54. Roy, K. and Prasad, S. (2000), Low-power CMOS VLSI Circuit Design, Wiley, New York, NY.
55. Schiff, L.I. (1955), Quantum Mechanics, 3rd ed., McGraw-Hill, New York, NY.
56. Scott, A.C., Chu, F.Y.F. and McLaughlin, D.W. (1973), The soliton: a new concept in applied science, Proceedings of the IEEE, Vol. 61 No. 10, pp. 1443-83.
57. Segev, M., Valley, G.C., Crosignani, B., DiPorto, P. and Yariv, A. (1994), Steady-state spatial screening solitons in photorefractive materials with external applied field, Physical Review Letters, Vol. 73, pp. 3211-4.
58. Shamir, J., Caulfield, H.J., Micelli, W. and Seymour, R.J. (1986), Optical computing and the Fredkin gates, Applied Optics, Vol. 25 No. 10, pp. 1604-7.
59. Shih, M. and Segev, M. (1996), Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons, Optics Letters, Vol. 21 No. 19, pp. 1538-40.
60. Siwak, P. (1998), Filtrons and their associated ring computations, International Journal of General Systems, Vol. 27 Nos 1/3, pp. 181-229.
61. Siwak, P. (1999), Iterons, fractals and computations of automata, International Conference on Computing Anticipatory Systems (CASYS), Vol. 465, pp. 45-63.
62. Stankovic, R.S. (1998), Spectral Transform Decision Diagrams in Simple Questions and Simple Answers, Nauka, Belgrade.
63. Steiglitz, K., Kamal, I. and Watson, A. (1988), Embedding computation in one-dimensional automata by phase coding solitons, IEEE Trans. Computers, Vol. 37 No. 2, pp. 138-45.
64. Takahashi, D. (1991), On a fully discrete soliton system, Proceedings of Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS), pp. 245-9.
65. Tikhonenko, V., Christou, J. and Luther-Davies, B. (1996), Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium, Physical Review Letters, Vol. 76, pp. 2698-702.
66. Wolfram, S. (Ed.)(1986), Theory and Application of Cellular Automata, World Scientific, Singapore.
67. m) for secure communication, Proceedings of International Symposium on Circuits and Systems (ISCAS), pp. 733-6.
68. Yan, Z. and Sarwate, D.V. (2002), Systolic architectures for finite field inversion and division, Proceedings of International Symposium on Circuits and Systems (ISCAS), pp. 789-92.
69. m), IEEE Trans. Comp., Vol. 52 No. 11, pp. 1514-9.
70. Yariv, A. (1989), Quantum Electronics, Wiley, New York, NY.
71. Yariv, A. and Yeh, P. (1984), Optical Waves in Crystals, Wiley, New York, NY.
72. Zaghloul, Y.A. and Zaghloul, A.R.M. (2006), Complete all-optical processing polarization-based binary logic gates and optical processors, Optics Express, Vol. 14 No. 21, pp. 9879-95.
73. Zheltikov, A.M. (2001), Reversible computations by coherent multiwave mixing: Toffoli-gate interpretation of Raman-excitation/CARS-probing experiments, Laser Physics, Vol. 11 No. 9, pp. 1049-51.