Switching Algebra Noninterference Based Spin Wave Computing

In recent years, Spin Waves (SWs) have emerged as a promising avenue for beyond-CMOS computing, offering potential advantages in terms of energy efficiency, scalability, and opening avenues towards novel computation paradigms. Until now, SW interference-based gates, for example, the 3 input majority gate (MAJ3), have been proposed and experimentally demonstrated, and an alternative computing paradigm, which relies on SW phase manipulation instead of SW interference has been proposed. However, state-of-the-art SW-based devices suffer from challenges that hinder the realization of larger-scale SW circuits. In this paper, we explore a different computing avenue that relies on Boolean algebra and introduce a SW Switch that makes use of the Voltage Controlled Magnetic Anisotropy (VCMA) effect to allow/block SW propagation. We introduce the device concept, verify its functionality by means of micromagnetic simulations, and perform a circuit-level analysis on EPFL Combinational Benchmarking Suite circuits. As no SW generation and SW read transducers energy consumption experimental data is available we evaluate their upper bound values for which SW implementations can outperform CMOS counterparts. We implement the circuits by means of state-of-the-art SW technologies and the proposed method, compute the upper bound values, and our results indicate that on average the proposal is increasing the upper bound by about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.2 \times$</tex>. Subsequently, we consider SW read transducers energy consumption estimates reported in the literature and argue that while they seem appropriate for evaluating SW Boolean switching gates they have to be multiplied with a factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m&gt;1$</tex> to capture the extra complexity of generating the output value for SW interference and Phase manipulation SW gates. Our evaluations indicate that the SW Switch-based approach reduces the energy consumption by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.2504 \times 1.4973 \times 1.7443 \times$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.9912 \times$</tex>, when compared to the interference approach, and by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.2478 \times, 1.4947 \times, 1.7416 \times$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.9886 \times$</tex>, when compared to the phase shifting approach, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m=1.25,1.5,1.75,2$</tex>, respectively. We finally highlight system level advantages of our proposal and conclude that SW Boolean switching gates are opening the most promising avenue towards energy effective SW computing.