Hardware Design for Autonomous Bayesian Networks.

Directed acyclic graphs or Bayesian networks that are popular in many AI-related sectors for probabilistic inference and causal reasoning can be mapped to probabilistic circuits built out of probabilistic bits (p-bits), analogous to binary stochastic neurons of stochastic artificial neural networks. In order to satisfy standard statistical results, individual p-bits not only need to be updated sequentially but also in order from the parent to the child nodes, necessitating the use of sequencers in software implementations. In this article, we first use SPICE simulations to show that an autonomous hardware Bayesian network can operate correctly without any clocks or sequencers, but only if the individual p-bits are appropriately designed. We then present a simple behavioral model of the autonomous hardware illustrating the essential characteristics needed for correct sequencer-free operation. This model is also benchmarked against SPICE simulations and can be used to simulate large-scale networks. Our results could be useful in the design of hardware accelerators that use energy-efficient building blocks suited for low-level implementations of Bayesian networks. The autonomous massively parallel operation of our proposed stochastic hardware has biological relevance since neural dynamics in brain is also stochastic and autonomous by nature.

Hardware implementation of Bayesian network building blocks with stochastic spintronic devices.

Bayesian networks are powerful statistical models to understand causal relationships in real-world probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the stochastic variables in a Bayesian network that encode the probability of occurrence of the associated event. This work presents an experimental demonstration of a Bayesian network building block implemented with inherently stochastic spintronic devices based on the natural physics of nanomagnets. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal under-layer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks.

Probabilistic Circuits for Autonomous Learning: A Simulation Study.

Modern machine learning is based on powerful algorithms running on digital computing platforms and there is great interest in accelerating the learning process and making it more energy efficient. In this paper we present a fully autonomous probabilistic circuit for fast and efficient learning that makes no use of digital computing. Specifically we use SPICE simulations to demonstrate a clockless autonomous circuit where the required synaptic weights are read out in the form of analog voltages. This allows us to demonstrate a circuit that can be built with existing technology to emulate the Boltzmann machine learning algorithm based on gradient optimization of the maximum likelihood function. Such autonomous circuits could be particularly of interest as standalone learning devices in the context of mobile and edge computing.

Integer factorization using stochastic magnetic tunnel junctions.

Conventional computers operate deterministically using strings of zeros and ones called bits to represent information in binary code. Despite the evolution of conventional computers into sophisticated machines, there are many classes of problems that they cannot efficiently address, including inference, invertible logic, sampling and optimization, leading to considerable interest in alternative computing schemes. Quantum computing, which uses qubits to represent a superposition of 0 and 1, is expected to perform these tasks efficiently1-3. However, decoherence and the current requirement for cryogenic operation4, as well as the limited many-body interactions that can be implemented, pose considerable challenges. Probabilistic computing1,5-7 is another unconventional computation scheme that shares similar concepts with quantum computing but is not limited by the above challenges. The key role is played by a probabilistic bit (a p-bit)-a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits in the same system using principles inspired by neural networks8. Here we present a proof-of-concept experiment for probabilistic computing using spintronics technology, and demonstrate integer factorization, an illustrative example of the optimization class of problems addressed by adiabatic9 and gated2 quantum computing. Nanoscale magnetic tunnel junctions showing stochastic behaviour are developed by modifying market-ready magnetoresistive random-access memory technology10,11 and are used to implement three-terminal p-bits that operate at room temperature. The p-bits are electrically connected to form a functional asynchronous network, to which a modified adiabatic quantum computing algorithm that implements three- and four-body interactions is applied. Factorization of integers up to 945 is demonstrated with this rudimentary asynchronous probabilistic computer using eight correlated p-bits, and the results show good agreement with theoretical predictions, thus providing a potentially scalable hardware approach to the difficult problems of optimization and sampling.

Multi-terminal spin valve in a strong Rashba channel exhibiting three resistance states.

In a strong spin-orbit interaction system, the existence of three resistance states were observed when two ferromagnetic (FM) contacts were used as current terminals while a separate normal metal contact pair was used as voltage terminals. This result is strikingly different from ordinary spin valve or magnetic tunnel junction devices, which have only two resistance states corresponding to parallel (RP) and antiparallel (RAP) alignments of the FM contacts. Our experimental results on a quantum well layer with a strong Rashba effect clearly exhibit unequal antiparallel states, i.e., RAP(1) > RP > RAP(2), up to room temperature. The three-states are observed without any degradation when the distance between the non-magnetic voltage probe and the ferromagnetic current probe was increased up to 1.6 mm.

Hardware emulation of stochastic p-bits for invertible logic.

The common feature of nearly all logic and memory devices is that they make use of stable units to represent 0's and 1's. A completely different paradigm is based on three-terminal stochastic units which could be called "p-bits", where the output is a random telegraphic signal continuously fluctuating between 0 and 1 with a tunable mean. p-bits can be interconnected to receive weighted contributions from others in a network, and these weighted contributions can be chosen to not only solve problems of optimization and inference but also to implement precise Boolean functions in an inverted mode. This inverted operation of Boolean gates is particularly striking: They provide inputs consistent to a given output along with unique outputs to a given set of inputs. The existing demonstrations of accurate invertible logic are intriguing, but will these striking properties observed in computer simulations carry over to hardware implementations? This paper uses individual micro controllers to emulate p-bits, and we present results for a 4-bit ripple carry adder with 48 p-bits and a 4-bit multiplier with 46 p-bits working in inverted mode as a factorizer. Our results constitute a first step towards implementing p-bits with nano devices, like stochastic Magnetic Tunnel Junctions.

Observation of current-induced, long-lived persistent spin polarization in a topological insulator: A rechargeable spin battery.

Topological insulators (TIs), with their helically spin-momentum-locked topological surface states (TSSs), are considered promising for spintronics applications. Several recent experiments in TIs have demonstrated a current-induced electronic spin polarization that may be used for all-electrical spin generation and injection. We report spin potentiometric measurements in TIs that have revealed a long-lived persistent electron spin polarization even at zero current. Unaffected by a small bias current and persisting for several days at low temperature, the spin polarization can be induced and reversed by a large "writing" current applied for an extended time. Although the exact mechanism responsible for the observed long-lived persistent spin polarization remains to be better understood, we speculate on possible roles played by nuclear spins hyperfine-coupled to TSS electrons and dynamically polarized by the spin-helical writing current. Such an electrically controlled persistent spin polarization with unprecedented long lifetime could enable a rechargeable spin battery and rewritable spin memory for potential applications in spintronics and quantum information.

Intrinsic optimization using stochastic nanomagnets.

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

Multi-Terminal Spin Valve on Channels with Spin-Momentum Locking.

It is experimentally established that charge current flowing in a channel with spin-momentum locking such as topological insulator surface states or Rashba interfaces induces a spin voltage, which can be electrically measured with a ferromagnetic contact along the current path. Using this fact in conjunction with Onsager reciprocity arguments, we make the surprising prediction that the anti-parallel resistance of a spin valve can be either larger or smaller than the parallel resistance depending on the direction of spin flow relative to the direction of spin-momentum locking. However, we argue that this remarkable signature of spin-momentum locking can only be observed in multi-terminal measurements. Two-terminal measurements in the linear response regime, will show a single anti-parallel resistance larger than the parallel resistance as commonly observed in channels without spin-orbit coupling. We support this result with detailed numerical calculations based on a semiclassical model that provides insight into the underlying physics.

A building block for hardware belief networks.

Belief networks represent a powerful approach to problems involving probabilistic inference, but much of the work in this area is software based utilizing standard deterministic hardware based on the transistor which provides the gain and directionality needed to interconnect billions of them into useful networks. This paper proposes a transistor like device that could provide an analogous building block for probabilistic networks. We present two proof-of-concept examples of belief networks, one reciprocal and one non-reciprocal, implemented using the proposed device which is simulated using experimentally benchmarked models.

Spin Funneling for Enhanced Spin Injection into Ferromagnets.

It is well-established that high spin-orbit coupling (SOC) materials convert a charge current density into a spin current density which can be used to switch a magnet efficiently and there is increasing interest in identifying materials with large spin Hall angle for lower switching current. Using experimentally benchmarked models, we show that composite structures can be designed using existing spin Hall materials such that the effective spin Hall angle is larger by an order of magnitude. The basic idea is to funnel spins from a large area of spin Hall material into a small area of ferromagnet using a normal metal with large spin diffusion length and low resistivity like Cu or Al. We show that this approach is increasingly effective as magnets get smaller. We avoid unwanted charge current shunting by the low resistive NM layer utilizing the newly discovered phenomenon of pure spin conduction in ferromagnetic insulators via magnon diffusion. We provide a spin circuit model for magnon diffusion in FMI that is benchmarked against recent experiments and theory.

Spin Circuit Model for 2D Channels with Spin-Orbit Coupling.

In this paper we present a general theory for an arbitrary 2D channel with "spin momentum locking" due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, -). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U-, and D-. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green's function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.

Manipulating quantum information with spin torque.

The use of spin torque as a substitute for magnetic fields is now well established for classical operations like the switching of a nanomagnet. What we are describing here could be viewed as an application of spin torque like effects to quantum processes involving single qubit rotations as well as two qubit entanglement. A key ingredient of this scheme is the use of a large number of itinerant electrons whose cumulative effect is to produce the desired qubit operations on static spins. Each interaction involves entanglement and collapse of wavefunctions so that the operation is only approximately unitary. However, we show that the non-unitary component of the operations can be kept below tolerable limits with proper design. As a capstone example, we present the implementation of a complete CNOT gate using the proposed spin potential based architecture, and show that the fidelity under ideal conditions can be made acceptably close to one.

Exponential Attenuation of Through-Bond Transmission in a Polyene: Theory and Potential Realizations.

An exponential falloff with separation of electron transfer and transport through molecular wires is observed and has attracted theoretical attention. In this study, the attenuation of transmission in linear and cyclic polyenes is related to bond alternation. The explicit form of the zeroth Green's function in a Hückel model for bond-alternated polyenes leads to an analytical expression of the conductance decay factor ß. The ß values calculated from our model (ß(CN) values, per repeat unit of double and single bond) range from 0.28 to 0.37, based on carotenoid crystal structures. These theoretical ß values are slightly smaller than experimental values. The difference can be assigned to the effect of anchoring groups, which are not included in our model. A local transmission analysis for cyclic polyenes, and for [14]annulene in particular, shows that bond alternation affects dramatically not only the falloff behavior but also the choice of a transmission pathway by electrons. Transmission follows a well-demarcated system of π bonds, even when there is a shorter-distance path with roughly the same kind of "electronic matter" intervening.

Modular Approach to Spintronics.

There has been enormous progress in the last two decades, effectively combining spintronics and magnetics into a powerful force that is shaping the field of memory devices. New materials and phenomena continue to be discovered at an impressive rate, providing an ever-increasing set of building blocks that could be exploited in designing transistor-like functional devices of the future. The objective of this paper is to provide a quantitative foundation for this building block approach, so that new discoveries can be integrated into functional device concepts, quickly analyzed and critically evaluated. Through careful benchmarking against available theory and experiment we establish a set of elemental modules representing diverse materials and phenomena. These elemental modules can be integrated seamlessly to model composite devices involving both spintronic and nanomagnetic phenomena. We envision the library of modules to evolve both by incorporating new modules and by improving existing modules as the field progresses. The primary contribution of this paper is to establish the ground rules or protocols for a modular approach that can build a lasting bridge between materials scientists and circuit designers in the field of spintronics and nanomagnetics.

Quantum interference in polyenes.

The explicit form of the zeroth Green's function in the Hückel model, approximated by the negative of the inverse of the Hückel matrix, has direct quantum interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of quantum interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments - if coherence in probe connections can be arranged - in some cases new destructive interference results, while in others one may have constructive interference. One such case may already exist in the literature.

Proposal for an all-spin logic device with built-in memory.

The possible use of spin rather than charge as a state variable in devices for processing and storing information has been widely discussed, because it could allow low-power operation and might also have applications in quantum computing. However, spin-based experiments and proposals for logic applications typically use spin only as an internal variable, the terminal quantities for each individual logic gate still being charge-based. This requires repeated spin-to-charge conversion, using extra hardware that offsets any possible advantage. Here we propose a spintronic device that uses spin at every stage of its operation. Input and output information are represented by the magnetization of nanomagnets that communicate through spin-coherent channels. Based on simulations with an experimentally benchmarked model, we argue that the device is both feasible and shows the five essential characteristics for logic applications: concatenability, nonlinearity, feedback elimination, gain and a complete set of Boolean operations.

Use of negative capacitance to provide voltage amplification for low power nanoscale devices.

It is well-known that conventional field effect transistors (FETs) require a change in the channel potential of at least 60 mV at 300 K to effect a change in the current by a factor of 10, and this minimum subthreshold slope S puts a fundamental lower limit on the operating voltage and hence the power dissipation in standard FET-based switches. Here, we suggest that by replacing the standard insulator with a ferroelectric insulator of the right thickness it should be possible to implement a step-up voltage transformer that will amplify the gate voltage thus leading to values of S lower than 60 mV/decade and enabling low voltage/low power operation. The voltage transformer action can be understood intuitively as the result of an effective negative capacitance provided by the ferroelectric capacitor that arises from an internal positive feedback that in principle could be obtained from other microscopic mechanisms as well. Unlike other proposals to reduce S, this involves no change in the basic physics of the FET and thus does not affect its current drive or impose other restrictions.

Spin-filter device based on the Rashba effect using a nonmagnetic resonant tunneling diode.

We propose an electronic spin-filter device that uses a nonmagnetic triple barrier resonant tunneling diode (TB-RTD). This device combines the spin-split resonant tunneling levels induced by the Rashba spin-orbit interaction and the spin blockade phenomena between two regions separated by the middle barrier in the TB-RTD. Detailed calculations using the InAlAs/InGaAs material system reveal that a splitting of a peak should be observed in the I-V curve of this device as a result of the spin-filtering effect. The filtering efficiency exceeds 99.9% at the peak positions in the I-V curve.