1 / 28

PORTLAND QUANTUM LOGIC GROUP

PORTLAND QUANTUM LOGIC GROUP. Optical Conservative Reversible and Nearly Reversible Gates. Integrated optics. Integrated optics offers a particularly interesting candidate for implementing parallel, reversible computing structures

aileen
Télécharger la présentation

PORTLAND QUANTUM LOGIC GROUP

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. PORTLAND QUANTUM LOGIC GROUP

  2. Optical Conservative Reversible and Nearly Reversible Gates

  3. Integrated optics • Integrated optics offers a particularly interesting candidate for implementing parallel, reversible computing structures • These structures operate in closer correspondence with the underlying microphysical laws which presume non-dissipative interactions and global interconnections.

  4. Zero energy can be dissipated internally • Dissipation in such circuits would arise only in reading the output, which amounts for clearing the computer for further use. • Total decoupling of computational and thermal modes. • Decoupling is achieved by: • reversing the computation after the results have been computed, • restoring the circuit to its initial configuration

  5. In optical and superconducting devices the decoupling between mechanical interaction modes and thermal modes can be effectively achieved. • For instance, isolation from thermal degrees of freedom occurs for: • 1. conservative-logic inverse, • 2. product functions, • 3. identity function • In optical nonlinear interface it occurs for 1 and 2 • In supercomputing loops used as memory elements it occurs for 3

  6. This is described in E. Fredkin and T. Toffoli, “Conservative Logic”, Int. J.Theor. Phys. 21,219 (1982).

  7. Troubles with optical logic • When the gate can be implemented, the output power from the gate is so low that cascading of gates is not possible. • J. Shamir, H.J. Caulfield, W.J. Micelli, and R. J. Seymour, “Optical Computing and the Fredkin Gates” Appl. Optics. 25,1604 (1986) • K.M. Johnson, M.A. Handschy and L.A. Pagano-Stauffer, “Optical Computing and Image Processing with Ferro-Electric Liquid Crystals”, Opt. Engr. 26, 385 (1987). • R. Cuykendall and D. Millin, “Limitations to Optical Fredkin Circuits”, OSA Tech Digest Ser.11, 70 (1987).

  8. Requirements for gates • No distinction can be made between the inputs. • Each must be of the same type (in this case optical) and at the same level • The unrestricted type of gate permits a significant reduction in circuit’s complexity. • The circuit must be both optically reversible and information-theory (logic) reversible.

  9. The device • An optical four-state nonlinear interface switching configuration is derived from the symmetry of an information-losless three-port structure • The device is: • bit-conservative • optically reversible • logically reversible • with dissipation related to the Kramers-Kronig inverse of the index of refraction

  10. The device • The device inherently possesses three-terminal characteristics: • insensitivity to line-noise fluctuations (maintains high contrast between transmitted and reflected beams) • cascadability through bit conservation, • fan-out by pumped transparentization, • free-space optical fan-in, • pumped (total internal) reflected inversion.

  11. A diffusive Kerrlike nonlinearity relating the intensity of the beam to the nonlinear mechanism density through the diffusion equation produces results which differ fundamentally from previous nondiffusive calculations. • Planar lattice-regularized layouts for binary adders • They reflect minimal reversible circuit designs.

  12. The dual-beam nonlinear interface • n 1 = n 10 • n 2 = n 10 -  n L + n 2NL(I0) • 90o inc sin-1 (n10-  n L + n 2NL(I0) )/ n10

  13. Fig. 2 Nonlinear interface with polarized signal beams of intensity I0 incident at glancing angle  0 or I0 0 or I0  n 2 = n 10 -  n L + n 2NL(I) n 1 = n 10 I0 or 0 2I0 or 0

  14. Fig. 3. Signal replication circuits consisting of an RNI and a half-wave plate. • Note that: • P or Qis the degraded signal • P and Q is the restored signal RNI = reversible non-linear interface Pv.Qh PQ’v.P’Qh PQv.PQh

  15. 1 h P v 1 v Q h Pv Qv Ph Qh Pv.Qh PQ’v.P’Qh RNI Fig. 3. Signal replication circuits consisting of an RNI and a half-wave plate. Half-wave plate • Note that: • P or Qis the degraded signal • P and Q is the restored signal /2 Pv Ph PQv.PQh Qv Qh

  16. Interaction gate implemented with a Fabry-Perot cavity Q P n = n0 + n 2NL(I) PQ PQ’ PQ P’Q

  17. AB AB A A’B A’B AB’ AB’ B AB AB Interaction Gate Inverse interaction Gate Interaction Gate A B In this gate the input signals are routed to one of two output ports depending on the values of A and B

  18. Priese Switch Gate Inverse Priese Switch Priese Switch CP CP P P C C C’P C’P C C In this gate the input signal P is routed to one of two output ports depending on the value of control signal C

  19. C C P C’P+CQ Q CP+C’Q Fredkin Gate Inverse Fredkin Gate Fredkin Gate C C P C’P+CQ Q CP+C’Q In this gate the input signals P and Q are routed to the same or exchanged output ports depending on the value of control signal C

  20. Q P C Fredkin Gate from Priese Switch Gates CQ  CP+CQ  CQ CP+  CQ CP C  CP

  21. Operation of a circuit from Priese Switches One red on inputs and outputs Conservative property CQ  CP+CQ Q=0  CQ CP+  CQ CP P=1 C=1 C  CP Two red on inputs and outputs Red signals are value 1

  22. Fredkin Gate from Interaction Gates C P Q C CP+  CQ  CP+ CQ

  23. Minimal Full Adder using Interaction Gates AB A A’B B AB’ AB Carry 0 A  B AB Sum A’B C AB’ AB

  24. Minimal Full Adder Using Priese Switch Gates AB A carry B B A’B sum C

  25. Minimal Full Adder Using Fredkin Gates A carry B C 1 sum 0 In this gate the input signals P and Q are routed to the same or exchanged output ports depending on the value of control signal C

  26. h v v h v h v h v,h v,h RNI Half-Adder Vertical polarization mirror horizontal polarization mirror

  27. ABv Ah A’Bv AB’h Bv Ah Bv ABh A’Bv + AB’h ABv + ABh Problem: Create such a circuit for the lattice of symmetric functions – not for exam.

  28. v v v h h 1h RNI Half-Adder Ah Bv A’Bv A’Bv 1h A’Bv A’Bh A’Bv + AB’h AB’h ABv AB’h Bv(A’B+A’B)h ABv + ABh ABv Problem: Create such a circuit for the lattice of symmetric functions – not for exam. Removes v Sum = (A’B+A’B)h Carry = ABh

More Related