Majority Logic Synthesis for Spin Wave Technology

Abstract

Abstract-Spin Wave Devices (SWDs) are promising beyond-CMOS candidates. Unlike traditional charge-based technologies, SWDs use spin as information carrier that propagates in waves. In this scenario, the logic primitive for computation is the majority gate. The majority gate has a greater expressive power than standard NAND/NOR gates, allowing SWD circuits to be more compact than CMOS, already at the logic level. Also, because there is not charge carrier transport, SWDs are estimated to have ultra-low power consumption. However, in order to exploit this opportunity, a native majority synthesis methodology is needed to fit the SWD technology needs. In this paper, we employ Majority-Inverter Graphs (MIGs) to naturally represent and synthesize SWD circuits. Thanks to the correspondence between the functionality of SWD primitive gates and MIG elements, MIG optimization intrinsically aims at minimum cost SWD implementations. Experimental results over MCNC benchmarks validate the efficiency of MIGs in SWD synthesis. As compared to traditional AND-Inverter Graph (AIG) synthesis, MIGs generate, on average, SWD circuits with 1.30× smaller area-delay-power product (ADP), improving their delay performance by 18%.

Majority-Inverter Graph: A New Paradigm for Logic Optimization

“…MIGs can fully harness the logic advantage over CMOS provided by these new switches, which is often a pivotal asset in the corresponding nanotechnologies. Preliminary experiments already shown superior results for SWD, ambipolar FET and ReRAM nanotechnologies [46], [49], [50]. Based on our studies and results so far, we foresee an even broader impact of MIGs in nanotechnology design.…”

“…In particular, various promising nanotechnologies realize devices behaving as majority voters. Specific examples include, but are not limited to, spin-wave device [46], quantum-dot cellular automata [47], DNA-based logic [48], ReRAM device [49] and ambipolar FET nanotechnologies [50]. For these nanotechnologies, MIGs are the natural and native circuit abstraction for automated design.…”

Logic Synthesis for Established and Emerging Computing

“…Whereas the results of using logic synthesis in various emerging technologies has been reported elsewhere [77]- [79] and reviewed in [11], we consider here the applications of logic synthesis methods to CMOS technology, optical computing (focusing on plasmonic logic), and quantum-dot cellular automata as well as quantum computing. This choice is motivated by the belief that CMOS will continue to be the mainstream technology, enhanced by emerging optical computing and communication technology.…”

“…Here, we describe as examples plasmonic-based devices and QCA, and we illustrate how logic synthesis data structures and algorithms described so far can be employed in order to realize logic circuits based on these new paradigms of computation. It is worth noting that logic synthesis for spin-based devices has already been extensively studied [11], [77]; nevertheless, the following discussion can be easily extended and applied to other majority-based nanotechnologies.…”

2-Output Spin Wave Programmable Logic Gate

“…By assuming that input SWs can have phases φ = 0 or φ = π their interference results in a SW with φ = 0 if the majority of inputs have φ = 0, and in a SW with φ = π otherwise. This implies that SW interaction provides natural support for, e.g., single gate 3-input majority function implementation, which in a CMOS technology based Boolean logic based implementation requires 18 transistors14,27 .…”