Abstract

Highly energy-efficient computing can be implemented by exploiting the physical nature of wave-particle duality (WPD) in coherent light propagation and detection. Requirements to satisfy the definition of WPD processors are elucidated and some of their properties evaluated with specific examples. Advantages and disadvantages are discussed and unique possible applications indicated.

© 1990 Optical Society of America

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References

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  1. R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191 (1961).
    [CrossRef]
  2. H. J. Bremermann, “Minimum energy requirements of information transfer and computing,” Int. J. Theor. Phys. 21, 203–217 (1982).
    [CrossRef]
  3. L. B. Levitin, “Physical limitations of rate, depth, and minimum energy in information processing,” Int. J. Theor. Phys. 21, 299–309 (1982).
    [CrossRef]
  4. C. H. Bennett, R. Landauer, “The fundamental physical limits of computation,” Sci. Am. 253, 48–56 (1985).
    [CrossRef]
  5. E. Fredkin, T. Foffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
    [CrossRef]
  6. J. Shamir, H. J. Caulfield, W. Miceli, R. J. Seymor, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
    [CrossRef] [PubMed]
  7. G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
    [CrossRef] [PubMed]
  8. H. J. Caulfield, J. Shamir, “Wave particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
    [CrossRef] [PubMed]
  9. K. K. Likharev, “Classical and quantum limitations on energy consumption in computing,” Int. J. Theor. Phys. 21, 311–326 (1982).
    [CrossRef]
  10. W. H. Zurek, “Reversibility and stability of information processing systems,” Phys. Rev. Lett. 53, 391–394 (1984).
    [CrossRef]
  11. D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. London Ser. A 400, 97–117 (1985).
    [CrossRef]
  12. A Peres, “Reversible logic and quantum computers,” Phys. Rev. A 32, 3266–3276 (1985).
    [CrossRef] [PubMed]
  13. R. P. Feynman, “Quantum mechanical computers,” Opt. News 11 (2), 11–20 (1985);Found. Phys. 16, 507–531 (1986).
    [CrossRef]
  14. H. J. Caulfield, “Parallel N4weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
    [CrossRef] [PubMed]
  15. J. Shamir, H. J. Caulfield, R. B. Johnson, “Massive holographic interconnections and their limitations,” Appl. Opt. 28, 311–324 (1989).
    [CrossRef] [PubMed]
  16. R. Kikuchi, B. H. Soffer, “Maximum entropy image restoration. I. The entropy expression,” J. Opt. Soc. Am. 67, 1656–1665 (1977).
    [CrossRef]
  17. See, for example, M. Garbuny, Optical Physics (Academic, New York, 1965).
  18. J. Shamir, “Fundamental speed limitations on parallel processing,” Appl. Opt. 26, 1567–1568 (1987).
    [CrossRef] [PubMed]
  19. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  20. F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]
  21. H. J. Caulfield, “Variable and fixed rank 1 N4 interconnections,” in Optical Computing ’88, J. W. Goodman, P. Chavel, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 564–569 (1988).
    [CrossRef]
  22. H. J. Caulfield, H.-I. Jeon, J. Brown, P. J. Werbos, “Variable and fixed rank 1 interconnections” (submitted to Appl. Opt.)
  23. H. J. Caulfield, “Role of the Horner efficiency in the optimization of spatial filters for optical pattern recognition,” Appl. Opt. 21, 4391–4392 (1982).
    [CrossRef] [PubMed]
  24. J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982).
    [CrossRef] [PubMed]
  25. L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 182–248.
  26. M. Bertolotti, “Photon statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974) pp. 41–74.
  27. E. L. Dereniak, D. G. Crowe, Optical Radiation Detectors (Wiley, New York, 1984).
  28. W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE (to be published).
  29. H. E. Elion, V. N. Morozov, Optoelectronic Switching Systems in Telecommunications and Computers (Dekker, New York, 1984).
  30. P. S. Guilfoyle, W. J. Willey, “Combinational logic based digital optical computing architectures,” Appl. Opt. 27, 1661–1673 (1988).
    [CrossRef] [PubMed]
  31. Z. Kohavi, Switching and Finite Automata Theory (McGraw-Hill, New York, 1978).
  32. P. J. M. van Laurhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
    [CrossRef]
  33. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

1989 (3)

1988 (1)

1987 (2)

1986 (1)

1985 (4)

C. H. Bennett, R. Landauer, “The fundamental physical limits of computation,” Sci. Am. 253, 48–56 (1985).
[CrossRef]

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. London Ser. A 400, 97–117 (1985).
[CrossRef]

A Peres, “Reversible logic and quantum computers,” Phys. Rev. A 32, 3266–3276 (1985).
[CrossRef] [PubMed]

R. P. Feynman, “Quantum mechanical computers,” Opt. News 11 (2), 11–20 (1985);Found. Phys. 16, 507–531 (1986).
[CrossRef]

1984 (2)

W. H. Zurek, “Reversibility and stability of information processing systems,” Phys. Rev. Lett. 53, 391–394 (1984).
[CrossRef]

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1982 (6)

H. J. Caulfield, “Role of the Horner efficiency in the optimization of spatial filters for optical pattern recognition,” Appl. Opt. 21, 4391–4392 (1982).
[CrossRef] [PubMed]

J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982).
[CrossRef] [PubMed]

E. Fredkin, T. Foffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

K. K. Likharev, “Classical and quantum limitations on energy consumption in computing,” Int. J. Theor. Phys. 21, 311–326 (1982).
[CrossRef]

H. J. Bremermann, “Minimum energy requirements of information transfer and computing,” Int. J. Theor. Phys. 21, 203–217 (1982).
[CrossRef]

L. B. Levitin, “Physical limitations of rate, depth, and minimum energy in information processing,” Int. J. Theor. Phys. 21, 299–309 (1982).
[CrossRef]

1977 (1)

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

1961 (1)

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191 (1961).
[CrossRef]

Aarts, E. H. L.

P. J. M. van Laurhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
[CrossRef]

Bennett, C. H.

C. H. Bennett, R. Landauer, “The fundamental physical limits of computation,” Sci. Am. 253, 48–56 (1985).
[CrossRef]

Bertolotti, M.

M. Bertolotti, “Photon statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974) pp. 41–74.

Bremermann, H. J.

H. J. Bremermann, “Minimum energy requirements of information transfer and computing,” Int. J. Theor. Phys. 21, 203–217 (1982).
[CrossRef]

Brown, J.

H. J. Caulfield, H.-I. Jeon, J. Brown, P. J. Werbos, “Variable and fixed rank 1 interconnections” (submitted to Appl. Opt.)

Cathey, W. T.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE (to be published).

Caulfield, H. J.

Crowe, D. G.

E. L. Dereniak, D. G. Crowe, Optical Radiation Detectors (Wiley, New York, 1984).

Dereniak, E. L.

E. L. Dereniak, D. G. Crowe, Optical Radiation Detectors (Wiley, New York, 1984).

Deutsch, D.

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. London Ser. A 400, 97–117 (1985).
[CrossRef]

Elion, H. E.

H. E. Elion, V. N. Morozov, Optoelectronic Switching Systems in Telecommunications and Computers (Dekker, New York, 1984).

Feynman, R. P.

R. P. Feynman, “Quantum mechanical computers,” Opt. News 11 (2), 11–20 (1985);Found. Phys. 16, 507–531 (1986).
[CrossRef]

Foffoli, T.

E. Fredkin, T. Foffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Fredkin, E.

E. Fredkin, T. Foffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Garbuny, M.

See, for example, M. Garbuny, Optical Physics (Academic, New York, 1965).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Guilfoyle, P. S.

Horner, J. L.

Jeon, H.-I.

H. J. Caulfield, H.-I. Jeon, J. Brown, P. J. Werbos, “Variable and fixed rank 1 interconnections” (submitted to Appl. Opt.)

Johnson, R. B.

Kikuchi, R.

Kohavi, Z.

Z. Kohavi, Switching and Finite Automata Theory (McGraw-Hill, New York, 1978).

Landauer, R.

C. H. Bennett, R. Landauer, “The fundamental physical limits of computation,” Sci. Am. 253, 48–56 (1985).
[CrossRef]

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191 (1961).
[CrossRef]

Levitin, L. B.

L. B. Levitin, “Physical limitations of rate, depth, and minimum energy in information processing,” Int. J. Theor. Phys. 21, 299–309 (1982).
[CrossRef]

Likharev, K. K.

K. K. Likharev, “Classical and quantum limitations on energy consumption in computing,” Int. J. Theor. Phys. 21, 311–326 (1982).
[CrossRef]

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Mandel, L.

L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 182–248.

Miceli, W.

Miceli, W. J.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE (to be published).

Milburn, G. J.

G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
[CrossRef] [PubMed]

Morozov, V. N.

H. E. Elion, V. N. Morozov, Optoelectronic Switching Systems in Telecommunications and Computers (Dekker, New York, 1984).

Peres, A

A Peres, “Reversible logic and quantum computers,” Phys. Rev. A 32, 3266–3276 (1985).
[CrossRef] [PubMed]

Seymor, R. J.

Shamir, J.

Soffer, B. H.

van Laurhoven, P. J. M.

P. J. M. van Laurhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
[CrossRef]

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Wagner, K.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE (to be published).

Werbos, P. J.

H. J. Caulfield, H.-I. Jeon, J. Brown, P. J. Werbos, “Variable and fixed rank 1 interconnections” (submitted to Appl. Opt.)

Willey, W. J.

Yu, F. T. S.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Zurek, W. H.

W. H. Zurek, “Reversibility and stability of information processing systems,” Phys. Rev. Lett. 53, 391–394 (1984).
[CrossRef]

Appl. Opt. (8)

IBM J. Res. Dev. (1)

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191 (1961).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Int. J. Theor. Phys. (4)

H. J. Bremermann, “Minimum energy requirements of information transfer and computing,” Int. J. Theor. Phys. 21, 203–217 (1982).
[CrossRef]

L. B. Levitin, “Physical limitations of rate, depth, and minimum energy in information processing,” Int. J. Theor. Phys. 21, 299–309 (1982).
[CrossRef]

E. Fredkin, T. Foffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

K. K. Likharev, “Classical and quantum limitations on energy consumption in computing,” Int. J. Theor. Phys. 21, 311–326 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. News (1)

R. P. Feynman, “Quantum mechanical computers,” Opt. News 11 (2), 11–20 (1985);Found. Phys. 16, 507–531 (1986).
[CrossRef]

Phys. Rev. A (1)

A Peres, “Reversible logic and quantum computers,” Phys. Rev. A 32, 3266–3276 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
[CrossRef] [PubMed]

W. H. Zurek, “Reversibility and stability of information processing systems,” Phys. Rev. Lett. 53, 391–394 (1984).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. London Ser. A 400, 97–117 (1985).
[CrossRef]

Sci. Am. (1)

C. H. Bennett, R. Landauer, “The fundamental physical limits of computation,” Sci. Am. 253, 48–56 (1985).
[CrossRef]

Other (11)

H. J. Caulfield, “Variable and fixed rank 1 N4 interconnections,” in Optical Computing ’88, J. W. Goodman, P. Chavel, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 564–569 (1988).
[CrossRef]

H. J. Caulfield, H.-I. Jeon, J. Brown, P. J. Werbos, “Variable and fixed rank 1 interconnections” (submitted to Appl. Opt.)

L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 182–248.

M. Bertolotti, “Photon statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974) pp. 41–74.

E. L. Dereniak, D. G. Crowe, Optical Radiation Detectors (Wiley, New York, 1984).

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE (to be published).

H. E. Elion, V. N. Morozov, Optoelectronic Switching Systems in Telecommunications and Computers (Dekker, New York, 1984).

See, for example, M. Garbuny, Optical Physics (Academic, New York, 1965).

Z. Kohavi, Switching and Finite Automata Theory (McGraw-Hill, New York, 1978).

P. J. M. van Laurhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
[CrossRef]

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

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Figures (11)

Fig. 1
Fig. 1

Nature of the so-called speed squeeze in ultrafast computers.

Fig. 2
Fig. 2

Architecture for a coherent holographic interconnection network: LD, laser diode array; H, hologram array; SLM, input spatial light modulator; L’s, lenses with focal length f (not necessarily identical); D, detector array.

Fig. 3
Fig. 3

Architecture for partially incoherent interconnection network: LD, laser diode array; H, hologram array; D, detector array. Each hologram may establish connections to all output pixels.

Fig. 4
Fig. 4

Coherent source (S) is collimated by lens C. A plane wave illuminates the hologram matrix (H) with attached input spatial light modulator (SLM). Output is detected on detector array (D). The hologram procedes the SLM to minimize incidence angles over the SLM.

Fig. 5
Fig. 5

Imaging by a hologram element of size h from the hologram array (H) of previous figures. The hologram is designed to obtain an image point P at distance d.

Fig. 6
Fig. 6

Coherent Fourier correlator with N × N pixels for the input (I), filter (F), and detector (D) planes. The Fourier-transforming lenses (L’s) are situated at a focal distance from each plant. Light from any point, such as (1) and (2) in plane I, arrives at all points of plane D, such as (1) and (2).

Fig. 7
Fig. 7

Fully interconnected architecture. A two-dimensional input vector x2D is multiplied by a coding vector v2D on a spatial light modulator (SLM1). A diffuser (not shown) scatters the transmitted light uniformly over SLM2, which transmits the output vector u2D.

Fig. 8
Fig. 8

(a) Probability density of three Poisson distributions with means 〈n〉 = 40, 80, 120. (b) Integrated distributions of (a).

Fig. 9
Fig. 9

The same as Fig. 8 but with spacing in geometrical progression 〈n〉 = 10, 40, 90.

Fig. 10
Fig. 10

Diagrammatic version of a one-to-one parallel optical-digital-computing element using the operator method.

Fig. 11
Fig. 11

WPD control system. NN1 and NN2 are neural net processors.

Equations (33)

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sin θ o = sin θ i + λ / Λ .
sin θ o λ = cos θ o θ o λ = 1 Λ ,
Δ θ c Δ λ Λ cos θ o .
Δ p c d Δ θ c .
Δ p d = d Δ θ d λ d h ,
Δ θ c < Δ θ d , Δ λ Λ cos θ max < λ h
Δ λ λ < Λ cos θ max h .
h Λ > N ,
Δ λ λ < cos θ max N ,
Δ l = d 2 + ( N h ) 2 d = d ( 1 cos θ max 1 ) ,
λ d h 2 > ( Λ N ) 2 ,
Δ l > ( N Λ ) 2 λ ( 1 cos θ cos 1 ) ,
Δ l > λ N 2 ( sin θ max sin θ i ) 2 ( 1 cos θ max 1 ) .
l c λ 2 Δ λ ,
λ Δ λ > N 2 ( sin θ max sin θ i ) 2 ( 1 cos θ max 1 ) N 2 .
y = ( u v T ) x .
E wpd = m h ν ,
e wpd = E wpd c = m h ν c .
e d k T .
E d cKT .
e wpd = 10 5 k T N 4 + N 2 .
E wpd prac E wpd l slm i h q = m h ν l slm i h q .
E d prac 10 4 ckT 10 12 k T
e wpd = m h ν 2 N 2 ,
E d = 2 N 2 k T ,
E d E wpd 2 × 10 5 N 2 .
σ = n .
O = A 1 Ā 2 Ā 3 A 4 A 5 .
Ō = Ā 1 + A 2 + A 3 + Ā 4 + Ā 5 .
c 1 T = ( 00110110 ) , c 2 T = ( 10110101 ) , c 3 T = ( 00010110 ) , c 4 T = ( 01110100 ) , c 5 T = ( 01110111 ) , c 6 T = ( 00110110 ) , c 7 T = ( 01010111 ) .
Δ E Δ t > h 4 π .
Δ t > 1 4 π m ν .
Δ ϕ = 2 π ν Δ t > 1 2 m rad .

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