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 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

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

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

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 2.4 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

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 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

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 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