1. Reversible Computing
Architectural implementation using only reversible primitives
Perform logical operations in a reversible manner
May be used to implement classical logic
Able to write compilers that would run normal code
Could allow for scaling of classical logic beyond current foreseen limits

2. Circuit Level Requirements
Not destroy information
Inputs must be derivable by examining outputs
Balanced number of inputs and outputs
Use a physical process which allows operation in whichever direction driving force is applied
System must by physically reversible in addition to logically reversible
They are equivalent

3. Why bother with reversibility?
Process improvements are eventually a dead end
Energy usage will become prohibitive
Heat dissipation will become more problematic
Classical computer dissipates a lot of energy
Bulk electron processes
Many electrons used to do a single logical operation

4. Current Energy Usage Current Energy Dissipation Power density
Consider an average desktop processor
2 x 10^9 Hz Clock speed, 5 x 10^7 Logical Elements,
100 watts, 1.65 volts
10^-12 Joules/Logical operation
Power density
1 cm^2 die size
Assume 100 um thickness
10 Watts / mm^3

5. Does Not Scale Does not scale in the long term. Current tech
Target system
10^10 Hz Clock
10^17 Logical elements
Very ambitious
Classical architecture is not dead yet
Current tech
10^15 watts
Average Energy generation for 2004 in the USA
5 x 10^11 watts

6. Sources of Energy Loss Process Efficiency Entropic State Reduction
Implementation specific energy loss
Resistive losses
Radiative losses
Other sundry physical effects
Suffered by all computing architectures
Entropic State Reduction
Solved by reversible computing

7. High Efficiency Non-Reversible
Idealized non-reversible computer
Single electron logic gates
1 volt power supply
Dissipation of 40 x kT Joules per operation
K is Boltzmann's Constant ~1.4 x 10^-23 J/K
T is the operating Temperature
40 x kT ~= 1.6 x 10^8 Watts at room temperature
5 x 10^5 Watts at 1K
Intractable

8. Entropic Limits Non-Reversible computing must dissipate energy
Minimum ln(2) x kT Joules per Operation
1.3 x 10^4 watts
Non-Reversible logic gates must destroy information
2 input, 1 output gate
4 possible states input
2 possible states output
Other output is reduced to known state
Local Entropy is reduced
Heat is produced

9. Key Advantages Allows for the entropic waste to be minimized
Reduced waste heat

10. Fredkin Gate Inputs B & C are switched if A is present
Logically Complete
May be implemented using electrostatic repulsion

11. Fredkin Gate Implementation

12. Many Types of Reversible
The study of reversible logic is useful
Quantum computing is reversible
Some overlap of logical primatives

13. Helical? Electrons confined by rotating electric field
No use of quantum effects
Electrons are always at the bottom of a deep local potential well
Stable

14. Clock Distribution Rotating electric field is the clock signal
No clock distribution logic is required
One turn per clock cycle
Strength of electric field determines number of logic elements that may exist per turn
Will most likely require deep pipelining
Each turn of the helix is a pipeline stage

15. Physical Construction
Assume advanced manufacturing techniques
Such as required to make a single electron computer
Fluorinated Diamond in Vacuum
Would require very advanced manufacturing techniques
Less advanced materials are available
But would be less optimal
Allows for transport of both electrons and “holes”

16. Transport Loss
Electrons confined withing the helix at low temperature are nearly always at ground state
Very low scattering loss
Form potential such that energy delta for first excited state is several times larger then kT

17. Vibrational Losses Lattice vibration 2.4 x 10^-28 J / Cycle
F = 1.6 x 10 ^ -11 N
E = 10^8 V/M
Q = 1.6 x 10^-19
 = 3,500 kg / m^3
M = 10^12 pascals
2.4 x 10^-28 J / Cycle

18. Switching Loss Interacting electrons move out of ground state
Ground state is defined with respect to some potential energy function
If you know the state the electron will be in, the potential may be corrected such that it does not leave the ground state.
Interaction causes Acceleration
Results in radiation
10^-35 J / Interaction
Could use paired electron/hole
Reduce emission greatly
Little net charge acceleration

19. Dielectric losses Crystal dielectric loss
Electric field resonance
10^-34 J / Cycle
Structurally formed induced dipoles
Paths and surround have different dielectric constant
Insignificant

20. Input / Output Very strong electric field Optical interconnect
May not use electrical interconnects
Unless perpendicular
Optical interconnect
Photons incident could generate electron / hole pairs
Would probably generate bulk electrons
Or would be unreliable
Could then be fed into logical operations that would sort them
Electron / hole pairs could traverse logic half-phase offset
Recombine at the end to emit light and signal output

21. Error Rate Dependant upon time taken for switching operation
Given the simulated potential functions shown
5 ps switch results in error rate of 9.3 x 10^-11

22. Limits Should be able to decrease cycle time to 10^-14 seconds
At which point other fundamental limits are encountered
Consider energy change of Hamiltonian over switching operation
10 ^-20 J
Plank's constant, 6.6 x 10^-34 Joule seconds
Faster switching would require larger switching potential
Energy dissipation of 10^-27 J / cycle
Acoustic losses dominate
Lattice Vibration

23. Cooling Cost Boiling helium
84.5 Joules/Mole
4.7 x 10^-2 grams/second vaporized
Reduce pressure to reduce boiling point and achieve a temperature of 1.2K using only He4
$5/Liter
Liquid helium cost survey, January 2003, informal.
125 grams per liter

24. Operational Costs Reversible Non-Reversible
32 Liters per Day
$162 / day for cooling
Non-Reversible
3.84 x 10^6 kilowatt-hours per day
$0.10 / kilowatt-hour
$3.84 x 10^5 per day to run
Given current day prices, incentive exists.
With a large margin of uncertainly allowed