From Binary to Continuous Gates – and Back Again

Abstract

We describe how nuclear magnetic resonance (NMR) spectroscopy can serve as a substrate for the implementation of classical logic gates. The approach exploits the inherently continuous nature of the NMR parameter space. We show how simple continuous NAND gates with sin/sin and sin/sinc characteristics arise from the NMR parameter space. We use these simple continuous NAND gates as starting points to obtain optimised target NAND circuits with robust, error-tolerant properties. We use Cartesian Genetic Programming (CGP) as our optimisation tool. The various evolved circuits display patterns relating to the symmetry properties of the initial simple continuous gates. Other circuits, such as a robust XOR circuit built from simple NAND gates, are obtained using similar strategies. We briefly mention the possibility to include other target objective functions, for example other continuous functions. Simple continuous NAND gates with sin/sin characteristics are a good starting point for the creation of error-tolerant circuits whereas the more complicated sin/sinc gate characteristics offer potential for the implementation of complicated functions by choosing some straightforward, experimentally controllable parameters appropriately.