Exploration of the non-zero universe in instantaneous noise-based logic

Abstract Instantaneous noise-based logic (INBL) leverages the products and superpositions of uncorrelated noise signals to construct a 2N-dimensional Hilbert space (‘hyperspace’). This approach has been investigated for complex computational tasks traditionally associated with quantum computing, such as the Deutsch–Jozsa algorithm and phonebook search problems. In this study, we delve into the statistical characteristics of this computational framework. To facilitate simulations, we developed an INBL engine. N noise bits represented by 2N uncorrelated reference noises (random telegraph waves (RTWs)) form a 2N-dimensional space when used in superpositions. N-long binary strings are the hyperspace vectors formed by the products of the relevant reference noises that represent the corresponding bit values. The superpositions of the 2N possible products collectively define the 2N-dimensional universe. To prevent the occurrence of zeros in the time function of the universe signal, we implemented an asymmetric amplitude scheme for the 2N reference noise bits, utilizing different absolute amplitude values for the N uncorrelated waves of low (L) and high (H) bit values. The simulation results indicate that the distribution of discrete amplitudes within the universe waveform (time function) deviates from Gaussianity. This finding reinforces that we cannot assert independence among hyperspace vectors, even though they exhibit zero cross-correlation. Another observation is rare random spikes in the universe waveform; surprisingly, the distribution of their magnitudes (absolute values) conforms to a Gaussian curve. Both the magnitude and the mean frequency of these spikes depend on the number of noise bits N. As N increases, the number of discrete amplitude levels also rises, leading to a broader distribution. Conversely, with a growing N, both the relative magnitudes and frequency of spikes in the superposition diminish. The observed critical statistical properties can affect the implementation of INBL in practical applications, particularly by suggesting potential implications for the energy and supply voltage requirements in processors, although a detailed hardware-level energy model is beyond the scope of this work and is left for future study.