New noise-based logic representations to avoid some problems with time complexity

TL;DR

This paper proposes modified noise-based logic representations with time-shifted signals to overcome exponential time complexity issues, enabling faster hyperspace state identification similar to quantum computing efficiency.

Contribution

It introduces a novel time-shifted noise-based logic method that significantly improves speed and efficiency in state identification, addressing previous exponential complexity problems.

Findings

Exponential speedup in hyperspace state identification

Modified amplitudes prevent universe from being zero with high probability

Achieves O(N) complexity similar to quantum computing

Abstract

Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, the universe (uniform superposition) will be zero with high probability (non-zero with exponentially low probability) in the random-telegraph-wave representation thus the operations with the universe would require exponential time-complexity. To fix this deficiency, we modify the amplitudes of the signals of the L and H states and achieve an exponential speedup compared to the old situation. Another improvement concerns the identification of a single product (hyperspace) state. We introduce a time shifted noise-based logic, which is constructed by shifting each reference signal with a small time delay. This modification implies an exponential speedup of single hyperspace vector identification compared to the former case and it requires the same, O(N) complexity as in quantum computing.