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. For instance, isolation from thermal degrees of freedom occurs for:
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
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 Q is the degraded signal
P and Q is the restored signal
RNI = reversible non-linear interface
Pv.Qh
PQ’v.P’Qh
PQv.PQh

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

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

17. Inverse interaction GateB AB
A’B
AB’ AB
A’B
AB’ 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 Priese Switch Inverse Priese Switch CP CP P 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. Fredkin Gate Fredkin Gate Inverse Fredkin Gate P C CP+C’Q C’P+CQ Q C C
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. Fredkin Gate from Priese Switch GatesCQ Q
 CP+CQ
 CQ
CP+  CQ P C 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 GatesP Q C
CP+  CQ
 CP+ CQ

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

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

25. Minimal Full Adder Using Fredkin Gates
carry B C 1
sum
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. RNI Half-Adder h v v Vertical polarization mirror v,h v h h
horizontal polarization mirror

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

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