Hu, Xuan; Walker, Benjamin W.; Garcia-Sanchez, Felipe; Edwards, Alexander J.; Zhou, Peng; Incorvia, Jean A.; Paler, Alexandru; Frank, Michael P.; Friedman, Joseph S.
Magnetic skyrmions are nanoscale whirls of magnetism that can be propagated with electrical currents. The repulsion between skyrmions inspires their use for reversible computing based on the elastic billiard ball collisions proposed for conservative logic in 1982. In this letter, we evaluate the logical and physical reversibility of this skyrmion logic paradigm, as well as the limitations that must be addressed before dissipation-free computation can be realized.
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer’s Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.
To advance the energy efficiency of general digital computing far beyond the thermodynamic limits that apply to conventional digital circuits will require utilizing the principles of reversible computing. It has been known since the early 1990s that reversible computing based on adiabatic switching is possible in CMOS, although almost all the “adiabatic” CMOS logic families in the literature are not actually fully adiabatic, which limits their achievable energy savings. The first CMOS logic style achieving truly, fully adiabatic operation if leakage was negligible (CRL) was not fully static, which led to practical engineering difficulties in the presence of certain nonidealities. Later, “static” adiabatic logic families were described, but they were not actually fully adiabatic, or fully static, and were much slower. In this paper, we describe a new logic family, Static 2-Level Adiabatic Logic (S2LAL), which is, to our knowledge, the first CMOS logic family that is both fully static, and truly, fully adiabatic (modulo leakage). In addition, S2LAL is, we think, the fastest possible such family (among fully pipelined sequential circuits), having a latency per logic stage of one tick (transition time), and a minimum clock period (initiation interval) of 8 ticks. S2LAL requires 8 phases of a trapezoidal power-clock waveform (plus constant power and ground references) to be supplied. We argue that, if implemented in a suitable fabrication process designed to aggressively minimize leakage, S2LAL should be capable of demonstrating a greater level of energy efficiency than any other semiconductor-based digital logic family known today.
Josephson junctions, cryogenic CMOS, and adiabatic circuits were proposed as computing options decades ago, but never got traction due to competition from room-temperature CMOS. However, quantum computer control electronics naturally requires cryogenic temperatures, making a deeper investigation of these technologies timely.We argue that a technology hybrid and new system design principles are needed, which we illustrate with adiabatic cryo-CMOS circuits playing an unanticipated but very important role.Transistor redesign will lead to even further improvement beyond what's illustrated in this paper, but more research will be needed to know how much.
In a previous paper, we described a new abstract circuit model for reversible computation called asynchronous ballistic reversible computing (ABRC), in which localized information-bearing pulses propagate ballistically along signal paths between stateful abstract devices and elastically scatter off those devices serially, while updating the device state in a logically-reversible and deterministic fashion. The ABRC model has been shown to be capable of universal computation. In the research reported here, we begin exploring how the ABRC model might be realized in practice using single flux quantum solitons (fluxons) in superconducting Josephson junction (JJ) circuits. One natural family of realizations could utilize fluxon polarity to represent binary data in individual pulses propagating near-ballistically, along discrete or continuous long Josephson junctions or microstrip passive transmission lines, and utilize the flux charge (-1, 0, +1) of a JJ-containing superconducting loop with Φ0 < IcL < 2Φ0 to encode a ternary state variable internal to a device. A natural question then arises as to which of the definable abstract ABRC device functionalities using this data representation might be implementable using a JJ circuit that dissipates only a small fraction of the input fluxon energy. We discuss conservation rules and symmetries considered as constraints to be obeyed in these circuits, and begin the process of classifying the possible ABRC devices in this family having up to three bidirectional I/O terminals, and up to three internal states.
We measure the frequency dependence of a niobium microstrip resonator as a function of temperature from 1.4 to 8.4 K. In a 2-micrometer-wide half-wave resonator, we find the frequency of resonance changes by a factor of 7 over this temperature range. From the resonant frequencies, we extract inductance per unit length, characteristic impedance, and propagation velocity (group velocity). We discuss how these results relate to superconducting electronics. Over the 2 K to 6 K temperature range where superconducting electronic circuits operate, inductance shows a 19% change and both impedance and propagation velocity show an 11% change.
In an ongoing project at Sandia National Laboratories, we are attempting to develop a novel style of superconducting digital processing, based on a new model of reversible computation called Asynchronous Ballistic Reversible Computing (ABRC). We envision an approach in which polarized flux-ons scatter elastically from near-lossless functional components, reversibly updating the local digital state of the circuit, while dissipating only a small fraction of the input fluxon energy. This approach to superconducting digital computation is sufficiently unconventional that an appropriate methodology for hand-design of such circuits is not immediately obvious. To gain insight into the design principles that are applicable in this new domain, we are creating a software tool to automatically enumerate possible topologies of reactive, undamped Josephson junction circuits, and sweep the parameter space of each circuit searching for designs exhibiting desired dynamical behaviors. But first, we identified by hand a circuit implementing the simplest possible nontrivial ABRC functional behavior with bits encoded as conserved polarized fluxons, namely, a one-bit reversible memory cell with one bidirectional I/O port. We expect the tool to be useful for designing more complex circuits.
Dennard scaling ended a decade ago. Energy reduction by lowering supply voltage has been limited because of guard bands and a subthreshold slope of over 60mV/decade in MOSFETs. On the other hand, newly-proposed logic devices maintain a high on/off ratio for drain currents even at significantly lower operating voltages. However, such ultra low power technology would eventually suffer from intermittent errors in logic as a result of operating close to the thermal noise floor. Computational error correction mitigates this issue by efficiently correcting stochastic bit errors that may occur in computational logic operating at low signal energies, thereby allowing for energy reduction by lowering supply voltage to tens of millivolts. Cores based on a Redundant Residual Number System (RRNS), which represents a number using a tuple of smaller numbers, are a promising candidate for implementing energyefficient computational error correction. However, prior RRNS core microarchitectures abstract away the memory hierarchy and do not consider the power-performance impact of RNS-based memory addressing. When compared with a non-error-correcting core addressing memory in binary, naive RNS-based memory addressing schemes cause a slowdown of over 3x/2x for inorder/out-of-order cores respectively. In this paper, we analyze RNS-based memory access pattern behavior and provide solutions in the form of novel schemes and the resulting design space exploration, thereby, extending and enabling a tangible, ultra low power RRNS based architecture.
We review the physical foundations of Landauer’s Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and proper interpretation remain frequently misunderstood. Contrary to some misinterpretations of the Principle, the mere transfer of entropy between computational and non-computational subsystems can occur in a thermodynamically reversible way without increasing total entropy. However, Landauer’s Principle is not about general entropy transfers; rather, it more specifically concerns the ejection of (all or part of) some correlated information from a controlled, digital form (e.g., a computed bit) to an uncontrolled, non-computational form, i.e., as part of a thermal environment. Any uncontrolled thermal system will, by definition, continually re-randomize the physical information in its thermal state, from our perspective as observers who cannot predict the exact dynamical evolution of the microstates of such environments. Thus, any correlations involving information that is ejected into and subsequently thermalized by the environment will be lost from our perspective, resulting directly in an irreversible increase in thermodynamic entropy. Avoiding the ejection and thermalization of correlated computational information motivates the reversible computing paradigm, although the requirements for computations to be thermodynamically reversible are less restrictive than frequently described, particularly in the case of stochastic computational operations. There are interesting possibilities for the design of computational processes that utilize stochastic, many-to-one computational operations while nevertheless avoiding net entropy increase that remain to be fully explored.
Simulating HPC systems is a difficult task and the emergence of “Beyond CMOS” architectures and execution models will increase that difficulty. This document presents a “tutorial” on some of the simulation challenges faced by conventional and non-conventional architectures (Section 1) and goals and requirements for simulating Beyond CMOS systems (Section 2). These provide background for proposed short- and long-term roadmaps for simulation efforts at Sandia (Sections 3 and 4). Additionally, a brief explanation of a proof-of-concept integration of a Beyond CMOS architectural simulator is presented (Section 2.3).
Conventional wisdom in the spacecraft domain is that on-orbit computation is expensive, and thus, information is traditionally funneled to the ground as directly as possible. The explosion of information due to larger sensors, the advancements of Moore's law, and other considerations lead us to revisit this practice. In this article, we consider the trade-off between computation, storage, and transmission, viewed as an energy minimization problem.
Most existing concepts for hardware implementation of reversible computing invoke an adiabatic computing paradigm, in which individual degrees of freedom (e.g., node voltages) are synchronously transformed under the influence of externallysupplied driving signals. But distributing these "power/clock" signals to all gates within a design while efficiently recovering their energy is difficult. Can we reduce clocking overhead using a ballistic approach, wherein data signals self-propagating between devices drive most state transitions? Traditional concepts of ballistic computing, such as the classic Billiard-Ball Model, typically rely on a precise synchronization of interacting signals, which can fail due to exponential amplification of timing differences when signals interact. In this paper, we develop a general model of Asynchronous Ballistic Reversible Computing (ABRC) that aims to address these problems by eliminating the requirement for precise synchronization between signals. Asynchronous reversible devices in this model are isomorphic to a restricted set of Mealy finite-state machines. We explore ABRC devices having up to 3 bidirectional I/O terminals and up to 2 internal states, identifying a simple pair of such devices that comprises a computationally universal set of primitives. We also briefly discuss how ABRC might be implemented using single flux quanta in superconducting circuits.
For more than 50 years, computers have made steady and dramatic improvements, all thanks to Moore’s Law—the exponential increase over time in the number of transistors that can be fabricated on an integrated circuit of a given size. Moore’s Law owed its success to the fact that as transistors were made smaller, they became simultaneously cheaper, faster, and more energy efficient. The payoff from this win-win-win scenario enabled reinvestment in semiconductor fabrication technology that could make even smaller, more densely-packed transistors. And so this virtuous cycle continued, decade after decade. Now though, experts in industry, academia, and government laboratories anticipate that semiconductor miniaturization won’t continue much longer—maybe 10 years or so, at best. Making transistors smaller no longer yields the improvements it used to. The physical characteristics of small transistors forced clock speeds to cease getting faster more than a decade ago, which drove the industry to start building chips with multiple cores. But even multi-core architectures must contend with increasing amounts of “dark silicon,” areas of the chip that must be powered off to avoid overheating.
Information loss from a computation implies energy dissipation due to Landauer’s Principle. Thus, increasing the amount of useful computational work that can be accomplished within a given energy budget will eventually require increasing the degree to which our computing technologies avoid information loss, i.e., are logically reversible. But the traditional definition of logical reversibility is actually more restrictive than is necessary to avoid information loss and energy dissipation due to Landauer’s Principle. As a result, the operations that have traditionally been viewed as the atomic elements of reversible logic, such as Toffoli gates, are not really the simplest primitives that one can use for the design of reversible hardware. Arguably, a complete theoretical framework for reversible computing should provide a more general, parsimonious foundation for practical engineering. To this end, we use a rigorous quantitative formulation of Landauer’s Principle to develop the theory of Generalized Reversible Computing (GRC), which precisely characterizes the minimum requirements for a computation to avoid information loss and the consequent energy dissipation, showing that a much broader range of computations are, in fact, reversible than is acknowledged by traditional reversible computing theory. This paper summarizes the foundations of GRC theory and briefly presents a few of its applications.
Industry's inability to reduce logic gates' energy consumption is slowing growth in an important part of the worldwide economy. Some scientists argue that alternative approaches could greatly reduce energy consumption. These approaches entail myriad technical and political issues.
We address practical limits of energy efficiency scaling for logic and memory. Scaling of logic will end with unreliable operation, making computers probabilistic as a side effect. The errors can be corrected or tolerated, but overhead will increase with further scaling. We address the tradeoff between scaling and error correction that yields minimum energy per operation, finding new error correction methods with energy consumption limits about 2× below current approaches. The maximum energy efficiency for memory depends on several other factors. Adiabatic and reversible methods applied to logic have promise, but overheads have precluded practical use. However, the regular array structure of memory arrays tends to reduce overhead and makes adiabatic memory a viable option. This paper reports an adiabatic memory that has been tested at about 85× improvement over standard designs for energy efficiency. Combining these approaches could set energy efficiency expectations for processor-in-memory computing systems.
Continuing to improve computational energy efficiency will soon require developing and deploying new operational paradigms for computation that circumvent the fundamental thermodynamic limits that apply to conventionally-implemented Boolean logic circuits. In particular, Landauer's principle tells us that irreversible information erasure requires a minimum energy dissipation of kT ln 2 per bit erased, where k is Boltzmann's constant and T is the temperature of the available heat sink. However, correctly applying this principle requires carefully characterizing what actually constitutes "information erasure" within a given physical computing mechanism. In this paper, we show that abstract combinational logic networks can validly be considered to contain no information beyond that specified in their input, and that, because of this, appropriately-designed physical implementations of even multi-layer networks can in fact be updated in a single step while incurring no greater theoretical minimum energy dissipation than is required to update their inputs. Furthermore, this energy can approach zero if the network state is updated adiabatically via a reversible transition process. Our novel operational paradigm for updating logic networks suggests an entirely new class of hardware devices and circuits that can be used to reversibly implement Boolean logic with energy dissipation far below the Landauer limit.