Artificial neural network circuits with Josephson devices

Harada Y., Hioe W., Goto E.

Flux transfer device theory is reviewed. In such devices, generalized magnetic flux, defined as the time integral of voltage, is used to describe the device characteristics. The Josephson junction and inductor are the main circuit elements in flux transfer devices, because they maintain a constant value for the time integral of voltage. Flux transfer devices are based on either an RF SQUID (superconducting quantum interference device) or a fluxon device. Four devices, including the parametric quantron and the quantum flux parametron, are reviewed as applications of the RF SQUID. The fluxon feedback oscillator and a soliton device are also reviewed as applications of fluxon devices. The quantum flux parametron is then described. The parametron principle and the fundamental properties of the quantum flux parametron such as gain, switching speed, and power dissipation are discussed. Logic circuits and a memory cell are also reviewed. A novel analog-to-digital converter is proposed as an application of the quantum flux parametron.< >

Hatano Y., Harada Y., Yamashita K., Tarutani Y., Kawabe U.

A fast Josephson circuit using a threshold logic is developed for application to a multiplier and a binary counter. The former is a typical combinational circuit and the latter is a typical sequential circuit. The junction and barrier materials used were Nb-AlO/SUB X/-Nb. An optimized asymmetric two-junction interferometer maximized the operating margin of the threshold gate. A speed-up junction was introduced to decrease the switching delay without sacrificing the operating margin. A dumping resistor, which was inserted parallel to the input signal line of the threshold gate between its two terminals, decreased the reflection of the input signal caused by the gate inductance, thereby ensuring the margin and speed. To demonstrate the high-speed possibility of the Josephson threshold logic, a high-speed experiment for the circuits was performed. The multiplier demonstrated 210-ps operation.

Haring D.R.

A multi-threshold element is one in which several thresholds are used to separate the true inputs from the false inputs. Many circuit elements and configurations can be described by this model. An approach, based on conventional single-threshold threshold elements, is developed for the analysis and synthesis of multithreshold threshold elements. It is shown that the basic properties of such elements are similar to conventional threshold elements, and that k-threshold threshold-element realizability of an arbitrary n-variable Boolean function can be related to conventional threshold-element realizability of a related (n+k-1)-variable Boolean function. Foundations for two basically different methods for the synthesis of a single-element realization of an arbitrary Boolean function are developed, as are procedures for transforming such a realization into both two-level and multilevel loop-free networks of k-threshold threshold elements k≥1. Every element in the networks has the identical weight vector for the independent variables, which is some-times desirable. The transformation technique is a useful approach to the synthesis of functions by networks of conventional threshold elements. It is proved that if the given function requires a k-threshold threshold element, then at least [k/2+I] conventional threshold elements in a two-level network or [1+log 2 k] such elements in a multilevel network are required. Transformations are given for corresponding minimum-gate networks. Electronic-circuit realizations of multi-threshold elements and some logical-design applications of the multi-threshold approach to network design are discussed. The latter indicate that this approach can be easy to use and can result in economical realizations.

Golden E.B., Semenov V.K., Tolpygo S.K.

Schegolev Andrey E., Bastrakova Marina V., Sergeev Michael A., Maksimovskaya Anastasia A., Klenov Nikolay V., Soloviev Igor

The extensive development of the field of spiking neural networks has led to many areas of research that have a direct impact on people’s lives. As the most bio-similar of all neural networks, spiking neural networks not only allow for the solution of recognition and clustering problems (including dynamics), but they also contribute to the growing understanding of the human nervous system. Our analysis has shown that hardware implementation is of great importance, since the specifics of the physical processes in the network cells affect their ability to simulate the neural activity of living neural tissue, the efficiency of certain stages of information processing, storage and transmission. This survey reviews existing hardware neuromorphic implementations of bio-inspired spiking networks in the ”semiconductor”, ”superconductor”, and ”optical” domains. Special attention is given to the potentials for effective ”hybrids” of different approaches.

Primavera B.A., Khan S., Adler S.R., Shainline J.M.

Feldhoff F., Toepfer H.

Shainline J.M., Primavera B.A., Khan S.

Superconducting optoelectronic loop neurons are a class of circuits potentially conducive to networks for large-scale artificial cognition. These circuits employ superconducting components including single-photon detectors, Josephson junctions, and transformers to achieve neuromorphic functions. To date, all simulations of loop neurons have used first-principles circuit analysis to model the behavior of synapses, dendrites, and neurons. These circuit models are computationally inefficient and leave opaque the relationship between loop neurons and other complex systems. Here we introduce a modeling framework that captures the behavior of the relevant synaptic, dendritic, and neuronal circuits at a phenomenological level without resorting to full circuit equations. Within this compact model, each dendrite is discovered to obey a single nonlinear leaky-integrator ordinary differential equation, while a neuron is modeled as a dendrite with a thresholding element and an additional feedback mechanism for establishing a refractory period. A synapse is modeled as a single-photon detector coupled to a dendrite, where the response of the single-photon detector follows a closed-form expression. We quantify the accuracy of the phenomenological model relative to circuit simulations and find that the approach reduces computational time by a factor of ten thousand while maintaining an accuracy of one part in ten thousand. We demonstrate the use of the model with several basic examples. The net increase in computational efficiency enables future simulation of large networks, while the formulation provides a connection to a large body of work in applied mathematics, computational neuroscience, and physical systems such as spin glasses.

Khan S., Primavera B.A., Chiles J., McCaughan A.N., Buckley S.M., Tait A.N., Lita A., Biesecker J., Fox A., Olaya D., Mirin R.P., Nam S.W., Shainline J.M.

Superconducting optoelectronic hardware could be used to create large-scale and computationally powerful artificial spiking neural networks. The approach combines integrated photonic components that offer few-photon, light-speed communication with superconducting circuits that offer fast, energy-efficient computation. However, the monolithic integration of photonic and superconducting devices is needed to scale this technology. Here we report superconducting optoelectronic synapses that are created by monolithically integrating superconducting nanowire single-photon detectors with Josephson junctions. The circuits perform analogue weighting and the temporal leaky integration of single-photon presynaptic signals. Synaptic weighting is implemented in the electronic domain allowing binary, single-photon communication to be maintained. Records of recent synaptic activity are locally stored as current in superconducting loops, and dendritic and neuronal nonlinearities are implemented with a second stage of Josephson circuitry. This hardware offers synaptic time constants spanning four orders of magnitude (hundreds of nanoseconds to milliseconds). The synapses are responsive to presynaptic spike rates exceeding 10 MHz and consume approximately 33 aJ of dynamic power per synapse event before accounting for cooling. This demonstration also introduces new avenues for realizing large-scale single-photon detector arrays. Monolithically integrated superconducting single-photon detectors and Josephson junctions can be used to create superconducting optoelectronic synapses with analogue weighting and temporal leaky integration of single-photon presynaptic signals

Primavera B.A., Shainline J.M.

Superconducting electronic circuits have much to offer with regard to neuromorphic hardware. Superconducting quantum interference devices (SQUIDs) can serve as an active element to perform the thresholding operation of a neuron's soma. However, a SQUID has a response function that is periodic in the applied signal. We show theoretically that if one restricts the total input to a SQUID to maintain a monotonically increasing response, a large fraction of synapses must be active to drive a neuron to threshold. We then demonstrate that an active dendritic tree (also based on SQUIDs) can significantly reduce the fraction of synapses that must be active to drive the neuron to threshold. In this context, the inclusion of a dendritic tree provides dual benefits of enhancing computational abilities of each neuron and allowing the neuron to spike with sparse input activity.

Schegolev A.E., Klenov N.V., Soloviev I.I., Gudkov A.L., Tereshonok M.V.

The popularity and diversity of artificial neural networks for various applications are ever increasing. The development of neural networks in the form of software models and hardware systems emphasizes their relevance and range of applicability, from a ten-minute Python code, an AlphaZero neural network, and intelligent image and speech recognition algorithms to IBM and Qualcomm neuromorphic chips and D-Wave quantum computing systems. The superconductor implementation of neural networks, along with the obvious advantages of superconductor technology in terms of energy efficiency and operating speed, makes it possible to combine a neural network and a superconducting quantum processor in one computing unit. In this case, the quantum core of a complex system can be used to learn a neural network by a global optimization method. It is noteworthy that the world’s leading IT companies clearly demonstrate the market’s focus on superconducting elements. The relevance of this direction is analyzed against a historical retrospective.

Primavera B.A., Shainline J.M.

Any large-scale spiking neuromorphic system striving for complexity at the level of the human brain and beyond will need to be co-optimized for communication and computation. Such reasoning leads to the proposal for optoelectronic neuromorphic platforms that leverage the complementary properties of optics and electronics. Starting from the conjecture that future large-scale neuromorphic systems will utilize integrated photonics and fiber optics for communication in conjunction with analog electronics for computation, we consider two possible paths toward achieving this vision. The first is a semiconductor platform based on analog CMOS circuits and waveguide-integrated photodiodes. The second is a superconducting approach that utilizes Josephson junctions and waveguide-integrated superconducting single-photon detectors. We discuss available devices, assess scaling potential, and provide a list of key metrics and demonstrations for each platform. Both platforms hold potential, but their development will diverge in important respects. Semiconductor systems benefit from a robust fabrication ecosystem and can build on extensive progress made in purely electronic neuromorphic computing but will require III-V light source integration with electronics at an unprecedented scale, further advances in ultra-low capacitance photodiodes, and success from emerging memory technologies. Superconducting systems place near theoretically minimum burdens on light sources (a tremendous boon to one of the most speculative aspects of either platform) and provide new opportunities for integrated, high-endurance synaptic memory. However, superconducting optoelectronic systems will also contend with interfacing low-voltage electronic circuits to semiconductor light sources, the serial biasing of superconducting devices on an unprecedented scale, a less mature fabrication ecosystem, and cryogenic infrastructure.

Goteti U.S., Zaluzhnyy I.A., Ramanathan S., Dynes R.C., Frano A.

Significance Designing neuromorphic hardware for cryoelectronics is an important area of research as the field of computing paradigms beyond complementary metal-oxide-semiconductor (CMOS) progresses. Superconductivity and metal−insulator transitions are two of the most celebrated emergent, collective properties found in quantum materials such as strongly correlated oxides. Here, we present simulations of artificial neural networks that can be designed by combining superconducting devices (e.g. Josephson junctions) with Mott metal−insulator transition−based tunable resistor devices. Our simulations show that 1) neurons and synapses can be seamlessly created, 2) their functions can be tuned via learning, and 3) controlling disorder by incorporating light ions enables exponential multiplicity of states. The results open up directions for incorporating emergent behavior seen in condensed matter into hardware design for artificial intelligence.

Feldhoff F., Toepfer H.

Neuromorphic and bio-inspired circuits have reached considerable attention since Moore's Law is coming to its limitations. Information processing in mammalian brains takes place in a far more energy-efficient manner and significantly faster than in the best computing architecture nowadays. We propose an approach to bring those benefits to a superconducting information processing circuit. Since the computation in a neuronal network is considered as analogue and the computation as digital, the design is grown around a Josephson comparator with its inherent non-linearity in the transfer function as the central information processing unit. Furthermore, a modified version of the Josephson Transmission Line is used to realize an adaptable coupling between neuron cells. This circuit design benefits of the noise in a 4.2 K environment and is therefore more resilient to noise and switching errors than conventional digital circuits. The proposed circuit behavior in a 2-neuron configuration and the integration in a network topology will be investigated.

Shainline J.M.

General intelligence involves the integration of many sources of information into a coherent, adaptive model of the world. To design and construct hardware for general intelligence, we must consider principles of both neuroscience and very-large-scale integration. For large neural systems capable of general intelligence, the attributes of photonics for communication and electronics for computation are complementary and interdependent. Using light for communication enables high fan-out as well as low-latency signaling across large systems with no traffic-dependent bottlenecks. For computation, the inherent nonlinearities, high speed, and low power consumption of Josephson circuits are conducive to complex neural functions. Operation at 4 K enables the use of single-photon detectors and silicon light sources, two features that lead to efficiency and economical scalability. Here, I sketch a concept for optoelectronic hardware, beginning with synaptic circuits, continuing through wafer-scale integration, and extending to systems interconnected with fiber-optic tracts, potentially at the scale of the human brain and beyond.

Buckley S.M., Tait A.N., Chiles J., McCaughan A.N., Khan S., Mirin R.P., Nam S.W., Shainline J.M.

We show several techniques for using integrated-photonic waveguide structures to simultaneously characterize multiple waveguide-integrated superconducting-nanowire detectors with a single fiber input. The first set of structures allows direct comparison of detector performance of waveguide-integrated detectors with various widths and lengths. The second type of demonstrated integrated-photonic structure allows us to achieve detection with a high dynamic range. This device allows a small number of detectors to count photons across many orders of magnitude in count rate. However, we find a stray light floor of -30 dB limits the dynamic range to three orders of magnitude. To assess the utility of the detectors for use in synapses in spiking neural systems, we measured the response with average incident photon numbers ranging from less than $10^{-3}$ to greater than $10$. The detector response is identical across this entire range, indicating that synaptic responses based on these detectors will be independent of the number of incident photons in a communication pulse. Such a binary response is ideal for communication in neural systems. We further demonstrate that the response has a linear dependence of output current pulse height on bias current with up to a factor of 1.7 tunability in pulse height. Throughout the work, we compare room-temperature measurements to cryogenic measurements. The agreement indicates room-temperature measurements can be used to determine important properties of the detectors.

Berggren K., Xia Q., Likharev K.K., Strukov D.B., Jiang H., Mikolajick T., Querlioz D., Salinga M., Erickson J.R., Pi S., Xiong F., Lin P., Li C., Chen Y., Xiong S., et. al.

Recent progress in artificial intelligence is largely attributed to the rapid development of machine learning, especially in the algorithm and neural network models. However, it is the performance of the hardware, in particular the energy efficiency of a computing system that sets the fundamental limit of the capability of machine learning. Data-centric computing requires a revolution in hardware systems, since traditional digital computers based on transistors and the von Neumann architecture were not purposely designed for neuromorphic computing. A hardware platform based on emerging devices and new architecture is the hope for future computing with dramatically improved throughput and energy efficiency. Building such a system, nevertheless, faces a number of challenges, ranging from materials selection, device optimization, circuit fabrication and system integration, to name a few. The aim of this Roadmap is to present a snapshot of emerging hardware technologies that are potentially beneficial for machine learning, providing the Nanotechnology readers with a perspective of challenges and opportunities in this burgeoning field.

Bakurskiy S., Kupriyanov M., Klenov N.V., Soloviev I., Schegolev A., Morari R., Khaydukov Y., Sidorenko A.S.

We present both theoretical and experimental investigations of the proximity effect in a stack-like superconductor/ferromagnetic (S/F) superlattice, where ferromagnetic layers with different thicknesses and coercive fields are made of Co. Calculations based on the Usadel equations allow us to find the conditions at which switching from the parallel to the antiparallel alignment of the neighboring F-layers leads to a significant change of the superconducting order parameter in superconductive thin films. We experimentally study the transport properties of a lithographically patterned Nb/Co multilayer. We observe that the resistive transition of the multilayer structure has multiple steps, which we attribute to the transition of individual superconductive layers with the critical temperature, Tc, depending on the local magnetization orientation of the neighboring F-layers. We argue that such superlattices can be used as tunable kinetic inductors designed for artificial neural networks representing the information in a “current domain”.