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arXiv:2010.15991 · IEEE Transactions on Applied Superconductivity

Reversible Fluxon Logic With Optimized CNOT Gate Components

Kevin D. Osborn, Waltraut Wustmann

Published Dec 2, 2020• 15 citations
arXivHTMLPDF

Abstract

Reversible logic gates were previously implemented in superconducting circuits as adiabatic-reversible gates, which are powered with a sufficiently slow clock. In contrast, we are studying ballistic-reversible gates, where fluxons serve to both encode the information and power the gates. No power is applied to the gate apart from the energy of the input fluxons, and the two possible flux polarities represent the bit states. Undamped long Josephson junctions (LJJs), where fluxons move at practically constant speed from inertia, form the input and output channels of the gates. LJJs are connected in the gates by circuit interfaces, which are designed to allow the ballistic scattering from input to output fluxon states, using the temporary excitation of a localized mode. The duration of the resonant scattering determines the operation time of the gate, approximately a few Josephson plasma periods. Due to the coherent conversions between fluxon and localized modes, the ballistic gates can be very efficient: In our simulations, only a few percent of the fluxon's energy are dissipated in the gate operation. Ballistic-reversible gates can be combined with other nonballistic gate circuits to extend the range of gate functionalities. Here, we describe how the cnot can be built as a structure that includes the Identity-else-Same-gives-not (IDSN) and store-and-launch (SNL) gates. The IDSN is a 2-b ballistic gate, which we describe and analyze in terms of equivalent 1-b circuits. The SNL is a clocking gate, which allows the storage of a bit and the clocked launch of a fluxon on a bit-state-dependent output path. In the cnot, the SNL gates provide the necessary routing and fluxon synchronization for the input to the IDSN gate.

DOI
10.1109/tasc.2020.3035344

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Reversible logic gates were previously implemented in superconducting circuits as adiabatic-reversible gates, which are powered with a sufficiently slow clock. In contrast, we are studying ballistic-reversible gates, where fluxons serve to both encode the information and power the gates. No power is applied to the gate apart from the energy of the input fluxons, and the two possible flux polarities represent the bit states. Undamped long Josephson junctions (LJJs), where fluxons move at practically constant speed from inertia, form the input and output channels of the gates. LJJs are connected in the gates by circuit interfaces, which are designed to allow the ballistic scattering from input to output fluxon states, using the temporary excitation of a localized mode. The duration of the resonant scattering determines the operation time of the gate, approximately a few Josephson plasma periods. Due to the coherent conversions between fluxon and localized modes, the ballistic gates can be very efficient: In our simulations, only a few percent of the fluxon's energy are dissipated in the gate operation. Ballistic-reversible gates can be combined with other nonballistic gate circuits to extend the range of gate functionalities. Here, we describe how the cnot can be built as a structure that includes the Identity-else-Same-gives-not (IDSN) and store-and-launch (SNL) gates. The IDSN is a 2-b ballistic gate, which we describe and analyze in terms of equivalent 1-b circuits. The SNL is a clocking gate, which allows the storage of a bit and the clocked launch of a fluxon on a bit-state-dependent output path. In the cnot, the SNL gates provide the necessary routing and fluxon synchronization for the input to the IDSN gate.
Compared to irreversible gate operations, reversible digital logic gates can provide a fundamental advantage in energy efficiency. Here we discuss previously discovered 1-bit ballistic reversible logic gates and new experimental plans to measure it. The gates consist of long Josephson junctions (LJJs) connected by a circuit interface. The gate dynamics evanescently extends into the LJJs to realize the physically resonant gate operation. It differs from known adiabatic superconducting gates because it does not work in the adiabatic limit. Depending on the gate type, that is the Identity or NOT gate, the polarity of the outgoing fluxon should be preserved or inverted, respectively. The dynamics of the scattering process, originally discovered in full numerical simulation, is understood using collective coordinate analysis. We plan to experimentally study how well a fluxon can travel ballistically towards the interface, and scatter with the designed gate operation. Here we present gate and SQUID-sensing layout designs for a NOT gate. The LJJ circuit layout uses niobium trilayer short junctions with connecting wiring for inductors. Part of the design includes the shunting capacitors at the gate interface which is key for the resonant dynamics in the gates.
Today's industrial digital logic gates are reaching a technological limit and meanwhile, superconducting circuits produce fundamentally different technologies for the future of digital computing. The standard logic is irreversible and yet superconducting circuits allow digital reversible logic with a much higher energy efficiency per gate operation. Previous reversible gate circuits were “adiabatic,” meaning that they used adiabatic-clocking waveforms for their operation power. However, we are studying logic starting from a ballistic model, where ftuxons enable gates using only energy from their inertia. Our ftuxons are defined in Long Josephson Junctions (LJJs) and may travel ballistically, similar to a particle with negligible damping. Once a ftuxon's energy approaches close enough to the gate, a resonance is induced at the gate and the ftuxon loses its definite topology. Gates are comprised of the (few Josephson-penetration-depth long) ends of LJJs and a connecting circuit interface. Only after the resonance does a ftuxon get formed and yield the gate result without external power: a ftuxon for bit-state 0 or an antiftuxon for bit-state 1. Through earlier analysis of the numerically discovered phenomena we find that dynamics can be described with ftuxon- and antiftuxon-like excitations at the ends of LJJs within the gate. The bit-switching action in our gates is resonant indicating fundamentally different dynamics than the classic model of adiabatic reversible circuits. Our ballistic Reversible Fluxon Logic (RFL) gates have no added damping and calculated energy efficiencies of over 97%. Thus in our dynamical process the “bit energy” is preserved. However, irreversible logic completely dissipates this at each operation (e.g., charging energy in CMOS or SFQ energy in irreversible SFQ logic). An RFL gate can achieve a fast gate operation since its resonance is only few JJ plasma periods. We also describe the CNOT in our technology. It is enabled by a couple of vital gates: A IDSN logic gate, similar to our other ballistic gates, and a Store-aNd-Launch (SNL) timing gate to ensure proper synchronization of the bits. The latter allows bit storage followed by launching of a data ftuxon using an adiabatic pulse from a clock ftuxon with lower energy than the data ftuxon for good CNOT efficiency.
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 suchnon-reversiblefluxon control circuits. First, thepolarity filter gateis a simple non-reversible gate that allows one polarity of fluxon to pass, while reflecting the other polarity. In theoffstate 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.
Single-flux quantum (SFQ) digital logic is typically energy efficient and fast, and logic that uses ballistic and reversible principles will provide a new platform for efficient computing. We are studying long Josephson junctions (LJJs), SFQs within them, and an SFQ detector, all intended for future ballistic logic gate experiments. Specifically, we launch low-energy SFQ into discrete LJJs, made from an array of 80 Josephson junctions (JJs) and connecting inductors. The component JJs have critical currents (IcI_{c}Ic​) of only 7.5μA\mu \text{A}μA. Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx47zJ.WhiletheSFQlauncherisfairlystandard,theSFQdetectorusesJJcriticalcurrentsofonly47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only47zJ.WhiletheSFQlauncherisfairlystandard,theSFQdetectorusesJJcriticalcurrentsofonly\approx161616\mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.
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 Φ0cL0to 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.