Fundamental Physics of Reversible Computing--An Introduction.
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In a previous study, 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 (SFQ) 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 (LJJs) or microstrip passive transmission lines (PTLs), and utilize the flux charge (-1, 0, +1) of a JJ-containing superconducting loop with Φ 0 < I c L < 2Φ 0 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 3 bidirectional I/O terminals, and up to 3 internal states.
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
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.
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Classical and quantum models of dynamically reversible computers are considered. Instabilities in the evolution of the classical 'billiard ball computer' are analyzed and shown to result in a one-bit increase of entropy per step of computation. 'Quantum spin computers', on the other hand, are not only microscopically, but also operationally reversible. Readoff of the output of quantum computation is shown not to interfere with this reversibility. Dissipation, while avoidable in principle, can be used in practice along with redundancy to prevent errors.
The reversible execution of C/C++ code has been a target of research and engineering for more than a decade as reversible computation has become a central notion in large-scale parallel discrete event simulation (PDES). The simulation models that are implemented for PDES are of increasing complexity and size and require various language features to support abstraction, encapsulation, and composition when building a simulation model. In this paper, we focus on parallel simulation models that are written with user-defined C++ abstractions and abstractions of the C++ Standard Library. We present an approach based on incremental state saving for establishing reversibility of C++ and an evaluation for a kinetic Monte-Carlo simulation implemented in C++. Although a significant runtime overhead is introduced with our technique, it is an enormous win that it allows using the entire C++ language, and has that code automatically transformed into reversible code to enable parallel execution with the Rensselaer’s optimistic simulation system (ROSS).
Computer program for reversion of cumulative binomial probability distribution
Preliminary results from a novel reversible computer model of monolayer nucleation and growth are compared with extant irreversible computer models of monolayer growth's early process stages. Attention is given to the microstructures resulting from direct impingement, the cluster density attributable to direct impingement, microstructures resulting from impingement combined with surface migration, and the cluster density attributable to impingement in combination with surface migration.
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.