Phase 2

Taking the final population of Phase 1, evolution was continued, still with only first-order tunnelling simulated. Whenever the fitness of the best individual reached a threshold of -0.25, the temperature was increased by 10mK. It can be seen in Fig. 7 that although these small temperature increases usually caused some loss in fitness, the population had enough residual performance for the evolutionary process to work on, in adapting the individuals to the new conditions. The fact that co-tunnelling and increased temperature both smear out the Coulomb blockade in a very similar way further supports the soundness of this approach. Higher-order tunnel events are thus lumped into a larger effective temperature.

Figure 7: Continued evolution, at increasing temperature. The solid upper line is best fitness (left axis), and the lower dotted line is temperature (right axis). The temperature was increased by 10mK whenever the fitness reached -0.25, then was held constant upon reaching 340mK.

Due to time constraints, the temperature was held constant once it reached 340mK, to allow a recognisable NOR-gate to be formed. When the experiment was terminated, the best circuit (Fig. 8) certainly would not work in a computational circuit, but can be seen to be roughly approximating the target NOR response 5.

Figure 8: The best circuit so far for 340mK.

Figure 9: The input/output relationship of the circuit evolved at 340mK (see Fig. 8). Top: Simulation only of first-order tunnelling events. Middle: Simulation including second-order tunnelling. Bottom: Simulation including third-order tunnelling.

The circuit has some interesting properties. Its response deteriorates only slightly if second-order tunnelling events are now included in the simulation, and there is no further degradation if third-order events are also modelled. The thermal response of the circuit, considering only first-order tunnelling, is fascinating. Fig. 10 shows that the behaviour deteriorates not only when the temperature is increased, but also when it is decreased. The best performance is seen at 340mK -- the temperature during the final stage of evolution. The simulation does not model thermal drift of the parameter values, so this curve implies that the circuit exploits or relies upon the particular thermal energies of the electrons at around 340mK. Further investigation is underway to verify the physical realism of this phenomenon, as it is possible that it arises as a simulation artifact.

Figure 10: The thermal response of the circuit evolved for 340mK (see Fig. 8).

Although we have not produced an ideal NOR gate, this thermal response indicates that evolution has been exploring the utilisation of the physical medium in ways not normally imagined.