In recent years, Spin Waves (SWs) have emerged as a promising CMOS alternative technology, and SW interference-based majority gates have been proposed and experimentally realized. In this paper, we pursue a different computation avenue and introduce a SW device able to evaluate 2×2 2D convolution, which is a fundamental element for the implementation of Convolutional Neural Networks (CNNs). Assuming that the window pixels are P = [p₁, p₂; p₃, p₄] and the kernel is K = [k₁, k₂; k₃, k₄] we introduce a device which evaluates the convolution result Σ_{i = 1}⁴ p_i k_i within the SW domain by leveraging SWs inherent mechanisms, i.e., information encoding in SW amplitude and phase, SW amplitude decay due to Gilbert damping, SW interference. After introducing the SW device structure we demonstrate its proper behaviour by means of micromagnetic simulations. We also present power consumption, area, and delay estimates and argue that due to the fact that our proposal does not rely on standard adders and multipliers, it can substantially outperform traditional CMOS-based convolution implementations.

Current Spin Wave (SW) state-of-the-art computing relies on wave interference for achieving low power circuits. Despite recent progress, many hurdles, e.g., gate cascading, fan-out achievement, still exist. In a previous work, we introduced a novel SW phase shift based computation paradigm and demonstrated that an n-input Threshold Logic Gate (TLG) can be implemented with n + 1 phase shifters operating on the same SW. In this paper we further develop this concept by introducing a phase shift amount reading method by means of parametric amplification. We make use of 3-input Majority Gate (MAJ3) as discussion vehicle and introduce a novel majority function evaluation approach which postpone the threshold related calculations to the gate output readout stage. Subsequently, we verify this principle by means of micromagnetic simulations and discus the results. Finally, we utilize the proposed MAJ3 gate to implement a collection of representative logic circuits from the EPFL Combinational Benchmarking Suite and evaluate and compare their area, energy consumption, and Energy Area Product (EAP) with the ones of 7 nm CMOS technology node based counterpart imple-mentations. Our estimations indicate that EAP_CMOS/EAP_SW average value is 5.25 and 2.2 for a SW transducer feature size of 20 nm and 30 nm, respectively.

While Spin Waves (SW) interaction provides natural support for low power Majority (MAJ) gate implementations many hurdles still exists on the road towards the realization of practically relevant SW circuits. In this paper we leave the SW interaction avenue and propose Threshold Logic (TL) inspired SW computing, which relies on successive phase rotations applied to one single SW instead of on the interference of an odd number of SWs. After providing a short TL inside we introduce the SW TL gate concept and discuss the way to mirror TL gate weight and threshold values into physical phase-shifter parameters. Subsequently, we design and demonstrate proper operation of a SW TL based Full Adder (FA) by means of micro-magnetic simulations. We conclude the paper by providing inside on the potential advantages of our proposal by means of a conceptual comparison of MAJ and TL based FA implementations.

Recent theoretical and experimental spintronics developments clearly indicate that Spin Waves (SW) interference based Majority gates (MAJ3) open an alternative road towards ultra low-power circuit implementations potentially capable to outperform CMOS counterparts. However, hurdles still exist, e.g., gate cascading, as due to the very nature of SW interference MAJ3 gates are not input output coherent, i.e., produce output waves with different amplitudes corresponding to ‘weak’ and ‘strong’ majority, which precludes their direct cascading within the SW domain. State of the art designs address this issue by means of hybrid SW-CMOS systems that make use on domain converters, which are energy expensive and diminish if not nullify the ultra-low power promise of the SW-based computing paradigm. In this paper we propose a gate cascading technique that rely on the natural SW amplitude decay while propagating through a magnetic conduit. We demonstrate the concept by constructing the building block MAJ3(MAJ3(In1,In2,In3),In4,In5) and verifying its correct behaviour by means of micromagnetic simulations. We evaluate the proposed design in terms of energy consumption, delay, and area, and our calculations indicate that, when compared with its domain conversion counterpart, our proposal consumes 49.5% less energy, at the expense of 48% area and 76.5% delay overhead, respectively.