Date post: | 21-Dec-2015 |
Category: |
Documents |
View: | 216 times |
Download: | 2 times |
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