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Reinforcement learning algorithms are used in a wide range of applications, from gaming and robotics to autonomous vehicles. In this paper we describe a set of reinforcement learning-based local weight update rules and their implementation in superconducting hardware. Using SPICE circuit simulations, we implement a small-scale neural network with a learning time of order one nanosecond. This network can be trained to learn new functions simply by changing the target output for a given set of inputs, without the need for any external adjustments to the network. In this implementation the weights are adjusted based on the current state of the overall network response and locally stored information about the previous action. This removes the need to program explicit weight values in these networks, which is one of the primary challenges that analog hardware implementations of neural networks face. The adjustment of weights is based on a global reinforcement signal that obviates the need for circuitry to back-propagate errors., Comment: 15 pages, 6 figures

Neuromorphic computing has the potential to further the success of software-based artificial neural networks (ANNs) by designing hardware from a different perspective. Current research in neuromorphic hardware targets dramatic improvements to ANN performance by increasing energy efficiency, speed of operation, and even seeks to extend the utility of ANNs by natively adding functionality such as spiking operation. One promising neuromorphic hardware platform is based on superconductive electronics, which has the potential to incorporate all of these advantages at the device level in addition to offering the potential of near lossless communications both within the neuromorphic circuits as well as between disparate superconductive chips. Here we explore one of the fundamental brain-inspired architecture components, the fan-in and fan-out as realized in superconductive circuits based on Josephson junctions. From our calculations and WRSPICE simulations we find that the fan-out should be limited only by junction count and circuit size limitations, and we demonstrate results in simulation at a level of 1-to-10,000, similar to that of the human brain. We find that fan-in has more limitations, but a fan-in level on the order of a few 100-to-1 should be achievable based on current technology. We discuss our findings and the critical parameters that set the limits on fan-in and fan-out in the context of superconductive neuromorphic circuits., Comment: 17 pages 10 figures

Motivated by the importance of magnetization dynamics in nanomagnets for the development and optimization of magnetic devices and sensors, we measured and modeled spin wave spectra in patterned elliptical nanomagnets. Ferromagnetic resonance spectra for multiple nanomagnets of Ni80Fe20 , fabricated by electron-beam lithography to have nominal short-axes of 200 nm or 100 nm, were measured by use of heterodyne magneto-optical microwave microscopy. Scanning electron microscope images taken of the same nanomagnets were used to define element shapes for micromagnetic simulations. Measured spectra show significant differences between nominally identical nanomagnets, which could be only partially attributed to uncontrolled shape variations in the patterning process, as evidence by the limited agreement between the measured and simulated spectra. Agreement between measurements and simulations was improved by including a zone of reduced magnetization and exchange at the edges of the nanomagnets in the simulations. Our results show that the reduction of shape variations between individual magnetic random-access memory elements can potentially improve their performance. However, unambiguous determination of materials parameters in nanomagnets based on analysis and modeling of spin wave spectra remains problematic.

Single flux quantum (SFQ) circuits form a natural neuromorphic technology with SFQ pulses and superconducting transmission lines simulating action potentials and axons, respectively. Here we present a new component, magnetic Josephson junctions, that have a tunablility and re-configurability that was lacking from previous SFQ neuromorphic circuits. The nanoscale magnetic structure acts as a tunable synaptic constituent that modifies the junction critical current. These circuits can operate near the thermal limit where stochastic firing of the neurons is an essential component of the technology. This technology has the ability to create complex neural systems with greater than 10^21 neural firings per second with approximately 1 W dissipation., Comment: 2016 IEEE International Conference on Rebooting Computing (ICRC)

We studied the microwave assisted magnetic reversal of 65 nm by 71 nm elliptical Ni80Fe20 nanomagnets. Hysteresis curves were measured by magneto-optical Kerr effect for a range of microwave frequencies and amplitudes. The coercive field Hc was reduced by 26% for an rf field of 0.08Hc when the microwave frequency coincided with the minimum of the experimentally determined ferromagnetic resonance frequency with varying dc field. The experimental results for the fractional reduction in Hc with rf field amplitude are in good agreement with numerical simulations for an array of interacting macrospins with a physically realistic shape anisotropy distribution

A time-resolved ferromagnetic resonance technique was used to investigate the magnetization dynamics of a 10 nm thin Permalloy film. The experiment consisted of a sequence of magnetic field pulses at a repetition rate equal to the magnetic systems resonance frequency. We compared data obtained by this technique with conventional pulsed inductive microwave magnetometry. The results for damping and frequency response obtained by these two different methods coincide in the limit of a small angle excitation. However, when applying large amplitude field pulses, the magnetization had a non-linear response. We speculate that one possible cause of the nonlinearity is related to self-amplification of incoherence, known as the Suhl instabilities., Comment: 23 pages, 8 figures, submitted to PRB