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Title: Addressing the Funding Gap in Energy-Efficient Computing: Research Overview and Program Management Philosophy

Addressing the Funding Gap in Energy-Efficient
Computing Research Overview and Program
Management Philosophy
  • By Michael P. FrankPresented to the National
    Science FoundationDirectorate for Computer
    Information Science EngineeringComputer
    Communication Foundations (CCF) DivisionMonday,
    July 10, 2006

Overview of Talk
  • Motivation
  • The Looming Energy Efficiency Crisis in Computing
  • and the related Funding Gap between government
  • The Science
  • Why something called Reversible Computing is
    really Our Only Hope for solving the problem
  • And why we need to start major research on it
  • Why Im Here
  • Convey my vision of CCF, the EMT program and how
    the field of Reversible Computing fits into them
  • Ideas on how I would help run the EMT program

  • The Coming Crisis in Computer Energy Efficiency

Major Motivation of my WorkThe Energy
Efficiency Crisis
  • The bulk of past improvements in practical
    computer performance have been fundamentally
    enabled by steady improvements in the energy
    efficiency of computation
  • Defined as the number of useful computational
    operations performed per unit of available energy
    dissipated into the form of waste heat
  • Unfortunately, an end to the past trend of steady
    energy efficiency improvements is now clearly
    within sight
  • Designs at many levels (devices, circuits,
    architectures, algorithms) for conventional
    computing are rapidly converging towards optimal
    design-point asymptotes, within a few-decade
  • Beyond which substantial further progress will
    not be possible, at least not within the
    conventional classical, irreversible computing
  • To circumvent the crisis, a radical paradigm
    shift in our models and structures for
    computation is required!
  • I will show why reversible computing will be an
    essential part of this.

Computings Rapid Climb
  • The raw performance efficiency characteristics
    of our information processing technologies
    (computing, storage, communication) have been
    improving at a steady, exponentially increasing
    rate over time, for at least the past 50 years
  • Due to Moores Law (integration scale of
    electronics doubles every 1-2 years) and related
    technology trends
  • Performance trends also span multiple pre-IC
    technologies (vacuum tubes, relays, etc.) going
    back 100 years or more
  • Each generation of performance improvements has
    reliably led to significant new
    information-processing applications becoming

Substantial Societal Impact
  • Economic measures of the nations ( worlds)
    economy, such as GDP, per-capita income, and
    standard of living have also improved
    exponentially (although at slower rates) over
    this same period
  • Its clear that a substantial portion of these
    gains was made possible by the introduction of
    new IT applications, itself made possible by raw
    technology improvements
  • Nearly every major industry today has relied on
    digital/ electronic technologies for a
    substantial portion of the productivity gains it
    has made over the last few decades
  • Effected either directly, or indirectly through
    its suppliers

These historical observations raise an important
  • We can arguably expect that the future rate of
    growth of the entire world economy will
    substantially depend on future trends in
    information technology efficiency
  • I.e., will our raw technologycapabilities
    flatten out,continue improvingsteadily, or
    accelerate even faster than before?

But, a Severe Problem
  • The energy efficiency (useful operations
    performed per unit energy dissipated) of all
    conventional information processing technologies
    will flatten out within the next few decades
  • This is true for fundamental and absolutely
    irrefutable physical reasons! (To be discussed)
  • As a consequence, the cost efficiency (ops
    performed per unit cost) and thus practical
    performance (e.g., FLOPS per dollar of annual
    operating budget) of systems will also flatten!
  • This is assuming only that the economic cost of
    energy will not soon enter a new era of rapid
    exponential decay
  • Which seems unlikely since, at present, energy
    costs are rising
  • If this flattening happens, it can be expected
    to have a substantial braking effect on the
    entire world economy!
  • This would be an extremely negative outcome,
    which we should try our best to avoid at all

Why Energy Efficiency of Conventional Computing
Must Flatten
  • The potential energy efficiency gains from all
    conventional sources are limited For example
  • Decrease logic signal energy by lowering logic
  • This has already reached a practical limit of on
    the order of 1V going to much lower voltages
    leads to excessive FET energy leakage
  • Also, signal energy is subject to thermodynamic
    limits to be discussed
  • Eliminate speculative execution and other
    unnecessary CPU activity
  • Soon, energy dissipation becomes dominated by
    necessary activity
  • Turn off unused functional units when not in use
    to avoid unnecessary power dissipation from
    leakage currents
  • Soon, power is dominated by active switching in
    units that are in use
  • Replace algorithms for general-purpose CPUs with
    FPGA configurations or special-purpose
  • This is quite helpful, but typically yields at
    most 100x savings
  • Find new high-level algorithms that require fewer
    total operations
  • This is great when possible, but as our
    algorithms improve, significantly better
    algorithms become harder and harder to find

Trend of Minimum Transistor Switching Energy
Based on Data from International Technology
Roadmaps for Semiconductors
Node numbers(nm DRAM hp)
Historical trendline
Conservative industry targets
CV2/2 gate energy, Joules
An Urgent Scientific Need
  • Given the above considerations, I would say that
    one of the most important basic research issues
    that our society needs the field of computer
    science engineering to address is to find a
    definitive answer to the following question
  • Can the introduction of new alternative,
    unconventional computing paradigms (such as
    reversible, quantum, and bio-inspired computing)
    realistically prevent or forestall the
    flattening of the information technology curve?
  • And if so, how exactly can this work?
  • My vision is that answering this question should
    be a primary scientific mission of the EMT
  • Although other applications are also important

The Science
  • Why Reversible Computing is Our Last, Great
    Hope for Continuing to Improve Computing

The von Neumann-Landauer (VNL) Bound
  • Physical theorem To lose, obliviously erase, or
    otherwise irreversibly forget 1 bits worth of
    known information involves/requires the eventual
    dissipation of at least kBT ln 2 amount of free
    energy to heat in an external environment at some
    temperature T.
  • kB here is Boltzmanns constant, 1.3810-23 J/K
    in energy/temperature units
  • First alluded to by John von Neumann, 1949
    clarified and proven by Rolf Landauer, 1961.

A simple proof of the VNL bound
  • Heres a simple proof, from basic thermodynamic
    facts known for gt100 years!
  • If known information becomes unknown, this is (by
    defn) an increase of entropy.
  • Because entropy is simply unknown physical
  • And, all information that is accessible to us is
    physical information anyway.
  • Standard units of information and entropy are
    simply logarithmic units
  • 1 bit log 2 ?b.logb2 (indefinite logarithm
    object), Boltzmanns constant kB log e
  • Therefore, in units of Boltzmanns constant, 1
    bit kB(log 2/log e) kB ln 2
  • Thus, the loss (forgetting) of 1 bit is, by
    definition, the very same thing as an increase of
    entropy by the amount kB ln 2.
  • Once entropy is created, it can never be
    destroyed (2nd law of thermodynamics)
  • This follows from the micro-scale reversibility
    of basic laws of (today quantum) mechanics
  • As entropy builds up in a system, its temperature
  • To operate sustainably without eventual meltdown,
  • The entropy generated must be expelled to an
    external environment.
  • To add entropy S to an environment at temperature
    T requires adding energy E ST to that
    environment - this is the very definition of
    thermodynamic temperature!
  • Thus, to forget a bit (i.e., permanently expel it
    into the environment) requires that we must
    eventually permanently commit energy kBT ln 2 to
    the environment (as heat).

An Essential Element of Future Paradigms
Reversible Computing
  • Basic idea (R. Landauer, 1961 C. Bennett,
  • Fundamental physics suggests that in principle
    there is no limit to the energy efficiency of
    computing technologies, although this is true
    only to the extent that we avoid performing
    irreversible operations that discard information
    during the computing process
  • But, it seems that with sufficient engineering
    effort, we can in principle approach, as closely
    as we care to, the limit of a reversible computer
    that discards no information and dissipates no
  • Our practical aim is not zero energy, just
    continued steady reductions!
  • Present status of reversible computing
  • Potential advantages/tradeoffs are reasonably
    well understood
  • Models early prototypes exist, but no practical
    systems yet
  • Of interest to other clusters Implementing this
    notion would eventually impact computer
    engineering CS at all levels!
  • From low-level physical device requirements up
    through circuit design, theory, architecture,
    languages, algorithms

Irreversible vs. Reversible Digital Operations
  • A typical irreversible digital operation
  • Regardless of the previous digital contents x of
    some circuit node or memory cell, destructively
    overwrite it with a given new value y.
  • A closely corresponding, but reversible
  • Reversibly transform the old physical state
    representing x in place to a new state the new
    value y.
  • The semantic difference is that the 2nd op can
    only be done if the old value x is known
  • This means, it can be reconstructed based on the
    new value y together with other available
  • This restricts the kinds of replacements that can
    be done reversibly
  • e.g., cant replace two bits a,b with the product
    ab and 1 other bit

bit bucket
Simple Electronic Implementations
  • Irreversible CLEAR (set to 0) operation
  • Without knowing if there is charge on node N,
    connect it to ground (logic 0 reference level)
  • The stored information is lost and the entire
    associated node energy E is dissipated to heat!
  • Reversible CLEAR(change from 1 to 0)
  • Given that N contains a 1, we connect it to a
    source that goes from 1 to 0 over time t gt tc
  • Only a fraction tc/t of the node energy E is
  • tc 2RC is a time constant
  • R resistance of path
  • C capacitance of node

Switch open
Switch closed
Node is charged upwith an amount E
Node dischargessuddenly,all info energy
arefully lost
Charge Q (2EC)1/2 flows out in a controlled way
over time t, dissipation Ediss I2Rt Q2R/t
(Adiabatic charge transfer)
Simulation Results (Cadence/Spectre)
  • Graph shows power dissipation vs. frequency
  • in 8-stage shift register.
  • At moderate frequencies (1 MHz),
  • Reversible uses lt 1/100th the power of
  • At ultra-low power (1 pW/transistor)
  • Reversible is 100 faster than irreversible!
  • Minimum energy dissip. per nFET is lt 1 eV!
  • 500 lower than best irreversible!
  • 500 higher computational energy efficiency!
  • Energy transferred is still 10 fJ (100 keV)
  • So, energy recovery efficiency is 99.999!
  • Not including losses in power supply, though

2LAL Two-level adiabatic logic (invented at UF,
1 nJ
100 pJ
Standard CMOS
10 aJ
10 pJ
1 aJ
1 pJ
Energy dissipated per nFET per cycle
1 eV
100 fJ
100 zJ
2LAL 1.8-2V
10 fJ
10 zJ
kT ln 2
1 fJ
1 zJ
100 aJ
100 yJ
Reversible and/or Adiabatic VLSI Chips Designed
_at_ MIT, 1996-1999
By EECS grad students Josie Ammer, Mike Frank,
Nicole Love, Scott Rixner,and Carlin Vieri under
CS/AI lab members Tom Knight and Norm Margolus.
Some Important Results in Reversible Computing
So Far
  • Landauer (IBM) 1961
  • The von Neumann limit of kT ln 2 energy
    dissipation per bit operation only holds for
    irreversible operations.
  • Lecerf 1963, Bennett (IBM) 1973
  • Computers that use only reversible operations are
    still Turing universal.
  • Fredkin Toffoli (MIT), 1980
  • Reversible computers can be implemented in an
    idealized classical physical model.
  • Feynman (CalTech), 1982
  • Reversible computers can be implemented in a
    simple quantum physical model.
  • This paper eventually spawned the field of
    quantum computing
  • Younis Knight (MIT), 1993
  • Pipelined, sequential logic circuits can be
    implemented in fully-reversible CMOS.
  • This paper helped to spawn the field of adiabatic
  • MIT Pendulum Project (Ammer, Frank, Knight, Love,
    Margolus, Rixner, Vieri), 1994-1999
  • Designed implemented fully reversible
    programmable circuits, general-purpose RISC
    architectures, high-level programming languages,
    and algorithms for a wide variety of classical CS
  • Frank (MIT) 1997-1999
  • When physical constraints are accounted for,
    reversible computers offer asymptotically lower
    energy, cost, and time complexity for broad
    classes of problems than conventional machines.
  • Frank (UF) 2000-2002
  • The advantages of reversible computing over
    conventional computing increase as small
    polynomials of the underlying technology
    characteristics The trends show reversible
    winning within decades for machines at usual

Important Open Research Challenges in Reversible
  • Fundamental research on practicability of
    reversible computing
  • (Physics) Can we invent post-transistor devices
    with lower leakage and energy coefficients?
  • This research requires cross-disciplinary
    collaboration with physicists
  • (Engineering) Can we tailor physical mechanisms
    to precisely execute complex trajectories
    (computations) with high energy-recovery
  • E.g. efficient resonators and power-clock
    distribution systems driving adiabatic logic.
    Collaboration with extremely skilled EEs is
  • (Structures) Can we design mostly-reversible
    architectures with low overhead for practical
    special-purpose applications, at least?
  • Existing general-purpose reversible architectures
    are highly suboptimal
  • (Theory) Can we reversibly emulate general
    irreversible algorithms with less space-time
    complexity overhead than presently known?
  • Oracle-based results suggest not, but more work
    is needed

The Funding Gap inEnergy-Efficient Computing
  • As a proposal writer, Ive found that reversible
    computing falls into a rather awkward, in-between
  • Because it aims to help a broad range of
    practical applications, and is well-motivated by
    basic physics, many scientists who evaluate RC
    proposals say it seems too practical to receive
    basic research funding, they expect its
    development should be funded by industry.
  • Yet, because RC is high-risk, very disruptive,
    and probably will take much longer than
    industrys traditional 10-year lab-to-fab time
    lag to develop and broadly adopt, industry has
    largely ignored it, in favor of more short-term
    approaches to save energy
  • The major risk that society faces in allowing
    this funding gap to persist is that if industry
    steps in too late, then workable, practical
    implementations of RC might not be ready in time
    to prevent performance growth from stalling
  • If there is even a brief stall, the loss of
    momentum could breed pessimism and choke off
    industrys will to continue innovating

Why Im Here
  • My vision of CCF, EMT, and how I and my field fit
    into it

Areas Covered by CCF
  • Emerging Models and Technologies (EMT)
  • Paradigms Nanocomputing, quantum computing,
    biologically inspired computing
  • I would add reversible computing to this list
  • Founds. of Comp. Procs. Artifs. (FCPA)
  • Structures Programming languages, computer
    architecture, VLSI design
  • Theoretical Foundations (TF)
  • Theory Models of computation, complexity,
    parallelism, algorithms, information theory

Some Highlights of My Related Educational
  • Early exposure to nanotech/nanocomputing concepts
  • Nanotechnology course, K. Eric Drexler, Stanford,
  • Solid general background in CS theory AI
  • BS in Symbolic Systems, Stanford, 1991
  • MS in EECS on Decision-Theoretic techniques in
    AI, MIT, 1994
  • Ph.D. proposal on DNA-based computing
  • MIT Lab for CS, 94-95
  • Fairly early exposure to Quantum Computing
  • Reviewed the field for MIT EECS Ph.D. area exam,
  • Ph.D. minor in conventional CMOS VLSI design
  • Designed had fabbed several chips, for courses
    Ph.D. work
  • Ph.D. work on Reversible Computing
  • Included development of nanocomputing models,
    complexity theory, architectures, programming
    languages, VLSI design

What I See As Some General Research Questions
Behind EMT
  • What are the fundamental physical limits of
    present future information processing
  • As opposed to the more abstract, algorithmic
    kinds of limits addressed by traditional
    theoretical CS
  • What fundamental changes to our underlying
    models/paradigms of computation may we need in
    order to fully harness emerging technologies?
  • New models based on physics (or chemistry,
  • How can practical considerations help to guide
    our exploration of the emerging technology
  • E.g., concerns with (at least estimates of)
    real-world cost, performance, energy efficiency,
    reliability, ease of use

Some Cross-Cutting Questions to other areas of
  • Cross-cutting to FCPA cluster
  • What would the emergence of new computing
    paradigms require in terms of new architectures,
    programming languages, HW design tools?
  • Cross-cutting to TF cluster
  • What impacts do emerging technologies have on
    theoretical CS areas such as models of
    computation, complexity theory, algorithm design,
    and parallel computing?

What are the Fundamental Physical Limits of
  • Fundamental laws of physics impose a variety of
    universal limits that hold true in all physically
    possible information processing technologies
  • Thermodynamic von Neumann/Landauer (VNL) lower
    bound of kT ln 2 (18 meV at room temperature) on
    energy dissipated per known bit that is discarded
    into a temperature-T environment.
  • However, this one could be avoided via reversible
  • Quantum performance limit (Margolus-Levitin
    bound) of at most a rate 2E/h (hPlancks
    constant) of useful bit operations in any
    device with an active energy of E.
  • This limit applies even to reversible quantum
  • There are also fundamental physical limits on
    information density and bandwidth, but I wont
    get into those here

What Changes to Our Models/Paradigms are Needed?
  • Two of the most important new paradigms
  • Reversible computing teaches us that overcoming
    the energy-efficiency crisis will eventually
    require an emphasis on reversible operations,
    impacting increasingly higher levels throughout
  • Quantum computing teaches us that the fastest
    known algorithms for certain classes of problems
    require machines that provide the ability to
    perform uniquely quantum operations.

New Paradigms for Computing
  • Reversible computing aims to directly circumvent
    the energy efficiency problem through the use of
    energy-conserving physical mechanisms for
    information processing
  • Quantum computing aims for dramatic algorithmic
    improvements for some types of problems, using
    shortcuts through state space made possible by
    nonclassical operations
  • Bio-inspired computing broadly includes
  • In vivo biological computing, e.g., bacteria
    genetically engineered to incorporate custom gene
    expression regulation networks
  • In vitro biochemistry-based computing such as DNA
    computing and related approaches
  • In silico but still biologically-inspired
    techniques such as digital analog neural
    networks, other analog approaches, neuromorphic
    computing, etc

New Paradigms in Relation to What I see as EMTs
  • Bio-inspired computing is interesting, but
    generally incapable of superseding the limits of
    conventional technology by very much
  • All realistic bio-inspired approaches could be
    simulated by conventional parallel digital
    machines with (at most) modest constant-factor
  • The motivation for bio-inspired computing must
    come from other directions
  • Quantum computing is nice if it can be made to
    work, but as far as we know, it is limited in its
    applicability to relatively narrow classes of
    problems (e.g., hidden subgroup, modest gains for
  • Its potential economic impact is therefore only a
    small fraction of that for all leading-edge
    computing in general
  • Research that aims to broaden its applicability
    is potentially worthwhile
  • Reversible computing is the only unconventional
    paradigm that might possibly break down the
    roadblocks to indefinite future improvement of
    computer efficiency and practical performance in
    general applications
  • Its future economic value is thus potentially
  • However, it is difficult to do, and still in its
    infancy! Much research is needed.

Some Other Motivations for Paradigms Covered by
  • Bio-inspired computing
  • In vivo computing Self-reproducing,
    self-organizing microbial systems for various
    clinical or industrial applications
  • In vitro computing Self-assembly of
  • Neural networks Applications in machine learning
  • Analog electronics Low-power signal processing
  • Quantum computing
  • Fast factoring etc. for cryptanalysis of PK
  • Strong information security via quantum
  • Fast, flexible, accurate simulation of quantum
    physical systems
  • Reversible computing
  • Reversible logic is already used in quantum
    computing, and has a few possible applications in
    other areas of CS
  • Security auditable/verifiable computation,
    resilient systems
  • Transaction rollback for concurrent systems
  • May conceivably provide useful angles for
    tackling complexity-theory questions
  • e.g., FACTORING?P iff ? a poly-time zero-garbage
    reversible alg. to multiply primes

Some Important Research Challenges in Quantum
  • Important experimental physics challenges
  • Develop new experimental setups for prototype
    quantum computers that can effectively suppress
    decoherence to the threshold for fault-tolerance
  • To enable more rapid improvement of machine sizes
  • Develop effective physical architectures for
    efficient qubit transfer execution of parallel
    quantum circuits
  • Important theory challenges
  • Better characterize the limits of applicability
    of quantum algorithms
  • Find major new categories of applications beyond
    the scope of the standard hidden subgroup /
    unstructured search algorithms
  • Resolve major open issues in quantum complexity
  • Comparisons between BQP vs. BPP and NP, etc.

Program Administration Ideas
  • My personal program management philosophy
  • Hands-on leadership, guiding steering the
    work of proposers reviewers based on my vision
    and understanding of the programs mission and
    the scientific needs of the fields that it
    touches on
  • Clarify the vision and goals of the funding
    program up-front with a technical white paper
    surveying important open scientific issues
  • Include motivation for and summaries of important
    open research problems, with references to the
  • Encourage proposal writers to address the listed
    issues, or else to thoroughly motivate their own
    alternative directions
  • Proactively seek out researchers whose
    background, skills, and research interests seem
    to mesh well with the clusters mission and
  • and encourage them to submit proposals to the
  • Encourage review panel members to carefully
    consider the quality thoroughness of the
    motivation section when evaluating the scientific
    merit of proposals
  • IMHO, too much of todays research is not
    sufficiently well-motivated

Educational Component
  • Strongly encourage proposers to include
    educational activities in their proposals,
  • Organizing of conferences
  • Writing of technical books textbooks
  • Writing of introductory books for popular
  • Even encourage submission of proposals for
    activity that is primarily educational in nature
  • There is an education gap in the areas I
    discussed also
  • Especially in reversible computing, which is
    still little known
  • Emphasize the need for educational materials that
    have a strong interdisciplinary perspective
  • E.g., integrating CS, EE, physics issues

  • Among the various unconventional computing
    technologies, there are strong reasons to believe
    that reversible computing has the greatest
    potential to make an enormous, vital, broad, and
    timely economic impact in coming decades
  • Yet, compared to areas such as DNA, quantum, nano
    and bacterial computing, it has received by far
    the least attention and funding!
  • One of my main motivations for working in
    reversible computing has been to correct the
    imbalance between the underlying importance of
    and popular attention to this field
  • However, my influence as a lone researcher in
    the trenches is limited No programs support
    this presently unfashionable field
  • I hope in my position at EMT to help to finally
    bring some much-needed funding and attention to
    this orphaned area, and help guide research in
    new, productive directions
  • While continuing support for well-motivated
    projects in other areas

  • End of Presentation Extra Slides Follow

Goals of Presentation
  • Convey my vision for research education
    advancements in areas covered by CCF
  • Emerging Models Technologies for Comp.
  • Foundations of Computing Processes Artif.
  • Theoretical Foundations
  • Discuss what I see as major challenges
  • some ideas on how to address them
  • Review my own scientific activities
  • briefly survey some related areas

Structure of Talk
  • Briefly introduce what I believe are some
    important scientific questions that CCF can work
    to address
  • Both within EMT, and potentially cross-cutting to
    other clusters within CCF, even to other
  • Engineering, physical sciences
  • Summarize some of my own past research that
    relates to these questions
  • Work done at MIT, Univ. of Florida, and Florida
  • List some related research challenges
  • Present some ideas/strategies for administration
    of CCF programs so as to facilitate scientific
    progress on these issues

Everyone Has It All Wrong!
  • As the talk proceeds,
  • Ill explain (in the proud MIT tradition) why
    most of the rest of the world is thinking about
    the future of computing in a completely
    wrong-headed way.
  • In particular,
  • The Low-Power Logic Circuit Designers have it all
  • The Semiconductor Process Engineers have it all
  • (Most) Device Physicists have it all wrong!

The von Neumann-Landauer (VNL) principle
  • John von Neumann, 1949
  • Claim The minimum energy dissipated per
    elementary (binary) act of information is kT ln
  • No published proof exists only a 2nd-hand
    account of a lecture
  • Rolf Landauer (IBM), 1961
  • Logically irreversible (many-to-one) bit
    operations must dissipate at least kT ln 2
  • Paper anticipated but didnt fully appreciate
    reversible computing
  • One proper (i.e. correct) statement of the
  • The oblivious erasure of a known logical bit
    generates at least k ln 2 amount of new entropy.
  • Releasing into environment at T requires kT ln 2
    heat emission.

Proof of the VNL Principle
  • The principle is occasionally questioned, but
  • Its truth follows absolutely rigorously (and even
    trivially!) from rock-solid principles of
    fundamental physics!
  • (Micro-)reversibility of fundamental physics
  • Information (at the microscale) is conserved
  • I.e., physical information cannot be created or
  • only transformed via reversible, deterministic
  • Thus, when a known bit is erased (lost,
    forgotten) it must really still be preserved
    somewhere in the microstate!
  • But, since its value has become unknown, it has
    become entropy
  • Entropy is just unknown/incompressible information

Types of Dynamical Processes
  • These animations illustrate how states transform
    in their configuration space, in
  • A nondeterministic process
  • One-to-many transformations
  • An irreversible process
  • Many-to-one transformations
  • Nondeterministic and irreversible
  • Deterministic and reversible
  • One-to-one transformations only!

Physics is Reversible!
  • Despite all of the empirical phenomenology
    relating to macro-scale irreversibility, chaos,
    and nondeterministic quantum events,
  • Our most fundamental and thoroughly-tested modern
    models of physics (e.g. the Standard Model) are,
    at bottom, deterministic reversible!
  • All of the observed nondeterministic and
    irreversible phenomena can still be explained
    within such models, as emergent effects.
  • Although classical General Relativity is argued
    by some researchers to have certain irreversible
  • The general consensus seems to be that well
    eventually find that the correct theory of
    quantum gravity will be reversible.

Reversible/Deterministic Physics is Consistent
with Observations
  • Apparent quantum nondeterminism can validly be
    understood as an emergent phenomenon, an expected
    practical result of permanent wavefunction
  • As illustrated e.g. in the many worlds and
    decoherent histories pictures
  • Even if a quantum wavefunction does not split
    permanently, its evolution in a large system can
    quickly become much too complex to track within
    our models
  • Thus we resort to using reduced density
    matrices, which discard some knowledge
  • The above effects, plus imprecision in our
    knowledge of fundamental constants, result in
    some practical unpredictability even for
    microscale systems
  • Thus entropy, for all practical purposes, tends
    to increase towards its maximum
  • Chaos (macro-scale nondeterminism) occurs when
    entropy at the microscale infects our ability to
    forecast the long-term evolution of macroscopic
  • A necessary consequence of the computation-univers
    ality of physics?
  • Meanwhile, averaging of many high-entropy
    microscopic details results in a smoothing
    effect that leads to irreversible evolution of

Reversible Computing
  • Wed like to design mechanisms that compute while
    producing as little entropy as possible
  • In order to minimize consumption of free energy /
    emission of heat to the environment
  • Losing known information necessarily results in a
    minimum k ln 2 entropy increase per bit lost, so
  • Lets consider what we can do using logically
    reversible (one-to-one) operations that dont
    lose information.
  • Such operations are still computationally
  • Lecerf (1963), Bennett (1973)

Conventional Gate Operations are Irreversible
(even NOT!)
  • Consider a computer engineers (i.e., real
    world!) Boolean NOT gate (a.k.a. logical
  • Specified function Destructively overwrite
    output nodes value with the logical complement
    of the input!

Space-time logic networkdiagram (not the same
New in
New out
In-Place NOT (Reversible)
  • Computer scientists (i.e., somewhat
    fictionalized!) in-place logical NOT operation
  • Specified operation Replace a given logic
    signal with its logical complement.
  • People occasionally confuse the irreversible
    inverter operation with a reversible in-place NOT
  • The same icon is sometimes used in spacetime

old bit
new bit
In-Place Controlled-NOT (cNOT)
  • Specified function Perform an in-place NOT on
    the 2nd bit if and only if the 1st bit is a 1.
  • Equiv., replace 2nd bit with XOR of 1st 2nd bits

Before Before After After
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
old data
new data
Early Universal Reversible Gates
  • Controlled-controlled-NOT (ccNOT)
  • A.k.a. Toffoli gate
  • Perform cNOT(b,c) iff a1.
  • Equiv., c c XOR (a AND b)
  • Controlled-SWAP (cSWAP)
  • A.k.a. Fredkin gate
  • Swap b with c iff a1.
  • Conserves 1s

The Adiabatic Principle
  • Applied physicists know that a wide class of
    physical transformations can be done
  • From Greek adiabatos, It shall not be passed
  • Used to mean, no passage of heat through an
    interface separating subsystems at different
  • Newer, more general meaning No increase of
  • Of course, exactly zero entropy increase isnt
    practically doable
  • In practice, adiabatic is used to mean that the
    entropy generation scales down proportionally as
    the process takes place more gradually.
  • The general validity of this 1/t scaling relation
    is enshrined in the famous adiabatic theorem of
    quantum mechanics.

Adiabatic Charge Transfer
  • Consider passing a total quantity of charge Q
    through a resistive element of resistance R over
    time t via a constant current, I Q/t.
  • The power dissipation (rate of energy diss.)
    during such a process is P IV, where V IR is
    the voltage drop across the resistor.
  • The total energy dissipated over time t is
    therefore E Pt IVt I2Rt (Q/t)2Rt
  • Note the inverse scaling with the time t.
  • In adiabatic logic circuits, the resistive
    element is a switch.
  • The switch state can be changed by other
    adiabatic charge transfers.
  • In simple FET-type switches, the constant factor
    (energy coefficient) Q2R appears to be subject
    to some fundamental quantum lower bounds.
  • However, these are still rather far away from
    being reached.

The Low-Power Design community has it all wrong!
  • Even (most of) the ones who know about adiabatics
    and even many who have done extensive amounts of
    research on adiabatic circuits still arent doing
    it right!
  • Watch out! 99 of the so-called adiabatic
    circuit designs published in the low-power design
    literature arent truly adiabatic, for one reason
    or another!
  • As a result, most published results (and even
    review articles!) dramatically understate the
    energy efficiency gains that can actually be
    achieved with correct adiabatic design.
  • Which has resulted in (IMHO) too little serious
    attention having been paid to adiabatic

Circuit Rules for True Adiabatic Switching
  • Avoid passing current through diodes!
  • Crossing the diode drop leads to irreducible
  • Follow a dry switching discipline (in the relay
  • Never turn on a transistor when VDS ? 0.
  • Never turn off a transistor when IDS ? 0.
  • Together these rules imply
  • The logic design must be logically reversible
  • There is no way to erase information under these
  • Transitions must be driven by a quasi-trapezoidal
  • It must be generated resonantly, with high Q
  • Of course, leakage power must also be kept
  • Because of this, the optimal design point will
    not necessarily use the smallest devices that can
    ever be manufactured!
  • Since the smallest devices may have insoluble
    problems with leakage.

Importantbut oftenneglected!
Conditionally Reversible Gates
  • Avoiding VNL actually only requires that the
    operation be one-to-one on the subset of states
    actually encountered in a given system
  • This allows us to design with gates that do
    conditionally reversible operations
  • That is, they are reversible if certain
    preconditions are met
  • Such gates can be built easily using ordinary
  • Example cSET (controlled-SET) and cCLR
    (controlled-CLR) operations can be implemented
    with a single digital switch (e.g. a CMOS
    transmission gate), with operation timing
    controlled by an externally-supplied driving
  • These operations are conditionally reversible, if
    preconditions are met

Space-time logic diagram
newout in
oldout 0
finalout 0
Reversible OR (rOR) from cSET
  • Semantics rOR(a,b)if ab, c1.
  • Set c1, if either a or b is 1.
  • Reversible if initially ab ? c.
  • Two parallel cSETs simultaneouslydriving a
    shared output busimplements the rOR operation!
  • This is a type of gate composition that was not
    traditionally considered.
  • Similarly, one can do rAND, and reversible
    versions of all Boolean operations.
  • Logic synthesis with theseis extremely

Hardware diagram
Spacetime diagram
a OR b
Semiconductor Process Engineers have it all wrong!
  • Everybody still thinks that smaller FETs
    operating at lower voltages will forever be the
    way to obtain ever more energy-efficient and more
    cost-efficient designs.
  • But if correct adiabatic design techniques are
    included in our toolbox, this is simply not true!
  • With good energy recovery, higher switching
    voltages (requiring somewhat larger devices)
    enable strictly greater overall energy
    efficiency! (and thus lower energy cost!)
  • This is due to the suppression of FET leakage
    currents exponentially with Vq/kT.
  • The hardware cost-performance overheads of this
    approach only grow polylogarithmically with the
    energy efficiency gains
  • Over time, we can expect the overheads will be
    overtaken by competitively-driven per-device
    manufacturing cost reductions
  • If devices better than FETs arent found,
  • then I predict an eventual bounce in device

The Need for Ballistic Processes
  • In order to achieve low overall entropy
    generation in a complete system,
  • Not only must the logic transitions themselves
    take place in an adiabatic fashion,
  • but also the components that drive and control
    the signal levels and timing of logic transitions
    (power clocks) must proceed reversibly along
    the desired trajectory.
  • Thus, we require a ballistic driving mechanism
  • One that proceeds under its own momentum along
    a desired trajectory with relatively little
    entropy increase.
  • Many concepts for such mechanisms have been
    proposed, but
  • Designing a sufficiently high-quality power-clock
    mechanism remains the major unsolved problem of
    reversible computing

Fredkin and Toffolis (1980) Billiard-Ball Model
  • 1st conceptual model of a ballistic physical
    computing process
  • Perfectly rigid billiard balls bounce off walls
    each other in digitally-precise trajectories
  • Shown to be capable of asymptotically efficient
    simulations of arbitrary reversible circuits in
    2D (extensible to 3D also)
  • Its idealized it would be chaotically unstable
    in practice
  • The addition of appropriate constraining
    mechanisms to prevent the balls from going off
    track or out of sync is viewed as a later step
  • Zurek argued that analogous quantum processes can
    avoid the chaos

Requirements for Energy-Recovering Clock/Power
  • All of the known reversible computing schemes
    require the presence of a periodic and globally
    distributed signal that synchronizes and drives
    adiabatic transitions in the logic.
  • For good system-level energy efficiency, this
    signal must oscillate resonantly and
    near-ballistically, with a high effective quality
  • Several factors make the design of a resonant
    clock distributor that has satisfactorily high
    efficiency quite difficult
  • Any uncompensated back-action of logic on
  • In some resonators, Q factor may scale
    unfavorably with size
  • Excess stored energy in resonator may hurt the
    effective quality factor
  • Theres no reason to think that its impossible
    to do it
  • But it is definitely a nontrivial hurdle, that we
    reversible computing researchers need to face up
    to, pretty urgently
  • If we hope to make reversible computing practical
    in time to avoid an extended period of stagnation
    in computer performance growth.

MEMS Resonator Concept
Arm anchored to nodal points of fixed-fixed beam
flexures,located a little ways away, in both
directions (for symmetry)

Phase 180 electrode
Phase 0 electrode
manytimes along y axis,all anchored to the
same flexure
MEMS Quasi-Trapezoidal Resonator 1st Fabbed
(Funding source SRC CSR program)
  • Post-etch process is still being fine-tuned.
  • Parts are not yet ready for testing

Drive comb
Would a Ballistic Computer be a Perpetual Motion
  • Short answer No, not quite!
  • Hey, give us some credit here!
  • Were hard-core thermodynamics geeks, we know
    better than that!
  • Two traditional (and impossible!) kinds of
    perpetual motion machines
  • 1st kind Increases total energy - Violates 1st
    law of thermo. (energy conservation)
  • 2nd kind Reduces total entropy - Violates 2nd
    law of thermo. (entropy non-decrease)
  • Another kind that might be possible in an ideal
    world, but not in practice
  • 3rd kind Produces exactly 0 increase in
  • Requires perfect knowledge of physical constants,
    perfect isolation of system from environment,
    complete tracking of systems global
    wavefunction, no decoherence, etc.
  • What were more realistically trying to build in
    reversible computing is none of the above, but
    only the more modest goal of a For-a-long-time
    Motion Machine
  • I.e., one that just produces as close to zero
    entropy (per op) as we can possibly achieve!
  • It would coast along for a while, but without
    energy input, it would eventually halt
  • Such a coasting machine can perform no net
    mechanical work in a complete cycle,
  • But it can potentially do a substantial amount of
    useful computational work!

Some Results on Scalability of Reversible
  • In a realistic physics-based model of computation
    that accounts for thermodynamic issues
  • When leakage is negligible and heat flux density
    is bounded,
  • Adiabatic machines asymptotically outperform
    irreversible machines (even per unit cost!) as
    problem sizes machine sizes are scaled up
  • But, the absolute speedup when total system power
    is unrestricted grows only as a small polynomial
    with the machine size
  • E.g., exponents of 1/36 or 1/18, depending on
    problem class
  • The speedup per unit surface area or
    (equivalently) per unit power dissipation grows
    at a somewhat faster (but still gradual) rate
  • E.g., with the 1/6 power of machine size
  • Even when leakage is non-negligible,
  • Adiabatic machines can still attain
    constant-factor (i.e., problem-size-independent)
    energy savings ( speedups at fixed power) that
    scale as moderate polynomials of the device
  • E.g., roughly with the transistor on-off ratio to
    at least the 0.39 power
  • Cost overheads from RC in these scenarios also
    grow, somewhat faster
  • But, we can hope that device costs will continue
    to decline over time

Bennetts 1989 Algorithmfor Worst-Case
k 3n 2
k 2n 3
Worst-Case Energy/Cost Tradeoff(Optimized
Bennett-89 Variant)
cost ? energy ?1.59
Spacetime cost blowup factor
Energy savings factor
(Most) Device Physicists have it all wrong!
  • Unfortunately, Id say gt90 of papers published
    on new logic device concepts (whether based on
    CNTs, spintronics, etc.) either ignore or
    dramatically neglect the key issue of the energy
    efficiency of logic operations
  • Even though, looking forward, this is absolutely
    the most crucial parameter limiting the practical
    performance of leading-edge computing systems!
  • And, even the rare few device physicists who
    study reversible devices dont seem to be talking
    to the analog/RF/µwave engineers who might help
    them solve the many subtle and difficult problems
    involved in building extremely high-quality
    energy-recovering power-clock resonators

Device-Level Requirements for Reversible Computing
  • A good reversible digital bit-device technology
    should have
  • Low amortized manufacturing cost per device, d
  • Important for good overall (system-level)
  • Low per-device level of static standby power
    dissipation Psb due to energy leakage,
    thermally-induced errors, etc.
  • This is required for energy-efficient storage
    devices, especially
  • but its still a requirement (to a lesser extent)
    in logic as well
  • Low energy coefficient cEt Edissttr (energy
    dissipated per operation, times transition time)
    for adiabatic transitions between digital states.
  • This is required in order to maintain a high
    operating frequency simultaneously with a high
    level of computational energy efficiency.
  • And thus maintain good hardware efficiency (thus
    good cost-performance)
  • High maximum available transition frequency fmax.
  • This is especially important for applications in
    which the latency from inherently serial
    computing threads dominates total operating costs

Plenty of Room forDevice Improvement
Power per device, vs. frequency
  • Recall, irreversible device technology has at
    most 3-4 orders of magnitude of
    power-performance improvements remaining.
  • And then, the firm kT ln 2 (VNL) limit is
  • But, a wide variety of proposed reversible device
    technologies have been analyzed by physicists.
  • With preliminary estimates of theoretical
    power-performance up to 10-12 orders of magnitude
    better than todays CMOS!
  • Ultimate limits are unclear.

.18µm CMOS
.18µm 2LAL
k(300 K) ln 2
Variousreversibledevice proposals
One Optimistic Scenario
40 layers, ea. w.8 billion activedevices,freq.
180 GHz,0.4 kT dissip.per device-op
e.g. 1 billion devices actively switching at3.3
GHz, 7,000 kT dissip. per device-op
Note that by 2020, there could be a factor of
20,000 difference in rawperformance per 100W
package. (E.g., a 100 overhead factor from
reversible design could be absorbed while still
showing a 200 boost in performance!)
A Call to Action
  • The world of computing is threatened by permanent
    raw performance-per-power stagnation in 1-2
  • We really should try hard to avoid this, if at
    all possible!
  • A wide variety of very important applications
    will be impacted.
  • Many more of the nations (and the worlds) top
    physicists and computer scientists must be
  • to tackle the great Reversible Computing
  • Urgently needed A major new fundin
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