Drawing from hats by noise-based logic

TL;DR

This paper introduces a noise-based logic scheme using asymmetric random telegraph waves to efficiently solve hat-drawing problems, demonstrating exponential speed-up and reduced complexity compared to deterministic methods.

Contribution

It presents a novel noise-based logic approach for combinatorial problems, leveraging superposition and stochasticity for exponential computational advantages.

Findings

Achieves exponential speed-up in identifying missing or known numbers in hats.

Requires exponentially less computational complexity than deterministic algorithms.

Utilizes superposition and stochasticity as key components for efficiency.

Abstract

We utilize the asymmetric random telegraph wave-based instantaneous noise-base logic scheme to represent the problem of drawing numbers from a hat, and we consider two identical hats with the first 2^N integer numbers. In the first problem, Alice secretly draws an arbitrary number from one of the hats, and Bob must find out which hat is missing a number. In the second problem, Alice removes a known number from one of the hats and another known number from the other hat, and Bob must identify these hats. We show that, when the preparation of the hats with the numbers is accounted for, the noise-based logic scheme always provides an exponential speed-up and/or it requires exponentially smaller computational complexity than deterministic alternatives. Both the stochasticity and the ability to superpose numbers are essential components of the exponential improvement.