Reversible logic schemes using flux solitons (fluxons) on long Josephson junctions (LJJs) have recently been proposed. The attraction of the fluxon is that it propagates ballistically along an LJJ until it encounters a change in the character of the LJJ, often a designed circuit element. Logic gates involve fluxons interacting with circuit elements and with other fluxons. However, testing of ballistic fluxon circuits requires other circuits outside the logic family to direct and control fluxon motion. We discuss two such non-reversible fluxon control circuits. First, the polarity filter gate is a simple non-reversible gate that allows one polarity of fluxon to pass, while reflecting the other polarity. In the off state both polarities reflect. Second, the polarity separator generalizes on the polarity filter concept and allows separation of the two fluxon polarities into different LJJs. We discuss simulations of these structures and possible applications.
In recent years we have been exploring a novel asynchronous, ballistic physical model of reversible computing, variously termed ABRC (Asynchronous Ballistic Reversible Computing) or BARC (Ballistic Asynchronous Reversible Computing). In this model, localized information-bearing pulses propagate bidi-rectionally along nonbranching interconnects between I/O ports of stateful circuit elements, which carry out reversible transformations of the local digital state. The model appears suitable for implementation in superconducting circuits, using the naturally quantized configuration of magnetic flux in the circuit to encode digital information. One of the early research thrusts in this effort involves the enumeration and classification, at an abstract theoretical level, of the distinct possible reversible digital functional behaviors that primitive BARC circuit elements may exhibit, given the applicable conservation and symmetry constraints in superconducting implementations. In this paper, we describe the motivations for this work, outline our research methodology, and summarize some of the noteworthy preliminary results to date from our theoretical study of BARC elements for bipolarized pulses, and having up to three I/O ports and two internal digital states.
In recent years we have been exploring a novel asynchronous, ballistic physical model of reversible computing, variously termed ABRC (Asynchronous Ballistic Reversible Computing) or BARC (Ballistic Asynchronous Reversible Computing). In this model, localized information-bearing pulses propagate bidi-rectionally along nonbranching interconnects between I/O ports of stateful circuit elements, which carry out reversible transformations of the local digital state. The model appears suitable for implementation in superconducting circuits, using the naturally quantized configuration of magnetic flux in the circuit to encode digital information. One of the early research thrusts in this effort involves the enumeration and classification, at an abstract theoretical level, of the distinct possible reversible digital functional behaviors that primitive BARC circuit elements may exhibit, given the applicable conservation and symmetry constraints in superconducting implementations. In this paper, we describe the motivations for this work, outline our research methodology, and summarize some of the noteworthy preliminary results to date from our theoretical study of BARC elements for bipolarized pulses, and having up to three I/O ports and two internal digital states.
Simple but mission-critical internet-based applications that require extremely high reliability, availability, and verifiability (e.g., auditability) could benefit from running on robust public programmable blockchain platforms such as Ethereum. Unfortunately, program code running on such blockchains is normally publicly viewable, rendering these platforms unsuitable for applications requiring strict privacy of application code, data, and results. In this work, we investigate using MPC techniques to protect the privacy of a blockchain computation. While our main goal is to hide both the data and the computed function itself, we also consider the standard MPC setting where the function is public. We describe GABLE (Garbled Autonomous Bots Leveraging Ethereum), a blockchain MPC architecture and system. The GABLE architecture specifies the roles and capabilities of the players. GABLE includes two approaches for implementing MPC over blockchain: Garbled Circuits (GC), evaluating universal circuits, and Garbled Finite State Automata (GFSA). We formally model and prove the security of GABLE implemented over garbling schemes, a popular abstraction of GC and GFSA from (Bellare et al., CCS 2012). We analyze in detail the performance (including Ethereum gas costs) of both approaches and discuss the trade-offs. We implement a simple prototype of GABLE and report on the implementation issues and experience.
Simple but mission-critical internet-based applications that require extremely high reliability, availability, and verifiability (e.g., auditability) could benefit from running on robust public programmable blockchain platforms such as Ethereum. Unfortunately, program code running on such blockchains is normally publicly viewable, rendering these platforms unsuitable for applications requiring strict privacy of application code, data, and results. In this work, we investigate using MPC techniques to protect the privacy of a blockchain computation. While our main goal is to hide both the data and the computed function itself, we also consider the standard MPC setting where the function is public. We describe GABLE (Garbled Autonomous Bots Leveraging Ethereum), a blockchain MPC architecture and system. The GABLE architecture specifies the roles and capabilities of the players. GABLE includes two approaches for implementing MPC over blockchain: Garbled Circuits (GC), evaluating universal circuits, and Garbled Finite State Automata (GFSA). We formally model and prove the security of GABLE implemented over garbling schemes, a popular abstraction of GC and GFSA from (Bellare et al., CCS 2012). We analyze in detail the performance (including Ethereum gas costs) of both approaches and discuss the trade-offs. We implement a simple prototype of GABLE and report on the implementation issues and experience.
Hu, Xuan; Walker, Benjamin W.; Garcia-Sanchez, Felipe; Edwards, Alexander J.; Zhou, Peng; Incorvia, Jean A.C.; 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.
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.
Computing uses energy. At the bare minimum, erasing information in a computer increases the entropy. Landauer has calculated %7E kBT log(2) Joules is dissipated per bit of energy erased. While the success of Moores law has allowed increasing computing power and efficiency for many years, these improvements are coming to an end. This project asks if there is a way to continue those gains by circumventing Landauer through reversible computing. We explore a new reversible computing paradigm, asynchronous ballistic reversible computing or ABRC. The ballistic nature of data in ABRC matches well with superconductivity which provides a low-loss environment and a quantized bit encoding the fluxon. We discuss both these and our development of a superconducting fabrication process at Sandia. We describe a fully reversible 1-bit memory cell based on fluxon dynamics. Building on this model, we propose several other gates which may also offer reversible operation.
Simple but mission-critical internet-based applications that require extremely high reliability and availability could potentially benefit from running on robust public programmable blockchain platforms such as Ethereum. Unfortunately, program code running on such blockchains is ordinarily publicly viewable, rendering these platforms unsuitable for applications requiring strict privacy of application code, data, and results. However, might it be possible to encode an application's business logic and data for these platforms in such a way that it becomes impossible for unauthorized parties to infer any meaningful information whatsoever about the semantics of the data, and the operations being performed on that data? In this report, we describe GABLE (Garbled Autonomous Bots Leveraging Ethereum), a system concept developed at Sandia that achieves this security goal in a limited, but still useful range of circumstances. GABLE, uses simple but effective algorithms to permit secure private execution of garbled state machines (and more efficient garbled circuits) on public computing resources. We give an example working implementation for garbled state machines, written using the Python and Solidity programming languages, and outline how our methods can be extended to support a more powerful garbled universal circuit model of computation. The capability embodied by the GABLE, system has significant potential applications, a few of which we discuss in this report.
As new memory technologies appear on the market, there is a growing push to incorporate them into future architectures. Compared to traditional DDR DRAM, these technologies provide appealing advantages such as increased bandwidth or non-volatility. However, the technologies have significant downsides as well including higher cost, manufacturing complexity, and for non-volatile memories, higher latency and wear-out limitations. As such, no technology has emerged as a clear technological and economic winner. As a result, systems are turning to the concept of multi-level memory, or mixing multiple memory technologies in a single system to balance cost, performance, and reliability.
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 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.
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.