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Reversible Computing

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

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Reversible Computing

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  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 • 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. • 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 • 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 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

  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 • 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 • 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

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