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

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

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

Current Energy Usage

● Current Energy Dissipation– 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

Does Not Scale

● Does not scale in the long term.– 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

Sources of Energy Loss

● Process Efficiency – Implementation specific energy loss

● Resistive losses● Radiative losses● Other sundry physical effects

– Suffered by all computing architectures● Entropic State Reduction

– Solved by reversible computing

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

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

Key Advantages

● Allows for the entropic waste to be minimized– Reduced waste heat

Fredkin Gate

● Inputs B & C are

switched if A is

present

● Logically Complete

● May be implemented

using electrostatic

repulsion

Fredkin Gate Implementation

Many Types of Reversible

● The study of reversible logic is useful– Quantum computing is reversible– Some overlap of logical primatives

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

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

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”

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

Vibrational Losses

● Lattice vibration– = 2 x 10 ^10– 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

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

Dielectric losses

● Crystal dielectric loss– Electric field resonance– 10^-34 J / Cycle

● Structurally formed induced dipoles– Paths and surround have different dielectric

constant● Insignificant

Input / Output

● Very strong electric field– 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

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

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

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

Operational Costs

● 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