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Abstract Probabilistic (p-) computing is a physics-based approach to addressing computational problems which are difficult to solve by conventional von Neumann computers. A key requirement for p-computing is the realization of fast, compact, and energy-efficient probabilistic bits. Stochastic magnetic tunnel junctions (MTJs) with low energy barriers, where the relative dwell time in each state is controlled by current, have been proposed as a candidate to implement p-bits. This approach presents challenges due to the need for precise control of a small energy barrier across large numbers of MTJs, and due to the need for an analog control signal. Here we demonstrate an alternative p-bit design based on perpendicular MTJs that uses the voltage-controlled magnetic anisotropy (VCMA) effect to create the random state of a p-bit on demand. The MTJs are stable (i.e. have large energy barriers) in the absence of voltage, and VCMA-induced dynamics are used to generate random numbers in less than 10 ns/bit. We then show a compact method of implementing p-bits by using VC-MTJs without a bias current. As a demonstration of the feasibility of the proposed p-bits and high quality of the generated random numbers, we solve up to 40 bit integer factorization problems using experimental bit-streams generated by VC-MTJs. Our proposal can impact the development of p-computers, both by supporting a fully spintronic implementation of a p-bit, and alternatively, by enabling true random number generation at low cost for ultralow-power and compact p-computers implemented in complementary metal-oxide semiconductor chips. 

An artificial neural network (ANN) inference involves matrix vector multiplications that require a very large number of multiply and accumulate operations, resulting in high energy cost and large device footprint. Stochastic computing (SC) offers a less resource-intensive ANN implementation with minimal accuracy loss. Random number generators (RNG) are required to implement SC in hardware. These can be realized through stochastic-magnetic tunnel junctions (s-MTJ), where the energy barrier to switch between the ‘up’ and ‘down’ states is designed to be small, enabling thermal noise to generate a random bit stream. While s-MTJs have previously been used to implement SC-ANNs, these studies have been limited to architectures with continuously varying (i.e.,analog) weights. In this work, we study the use of SC for matrix vector multiplication withquantizedsynaptic weights and quantized outputs. We show that a quantized SC-ANN, implemented by using experimentally obtained s-MTJ bitstreams and a limited number of discrete quantized states for both weights and hidden layer nodes in an ANN, can effectively reduce time (latency) and energy consumption in SC compared to an analog implementation, while largely preserving accuracy. We implemented quantization with 5 and 11 quantized states, along with SC configured with stochastic bitstream lengths of 100, 200, 300, 400, and 500 on neural networks with one hidden layer and three hidden layers. Inference was performed on the MNIST dataset for both training with SC and without SC. Training with SC provided better accuracy for all cases. For the shortest bitstream of 100 bits, the highest accuracies were 92% for one hidden layer and over 96% for three hidden layers. The overall system attained its peak accuracy of 96.82% using a 400 bit stochastic bitstream with three hidden layers. Our investigations demonstrate 9× improvement in latency and 2.6× improvement in energy consumption using the quantized SC approach compared to a similar s-MTJ based ANN architecture without quantization.