Entanglement, and unsorted database search in noise-based logic

TL;DR

This paper introduces noise-based logic algorithms for database search that achieve exponential speedup and zero error probability, offering advantages over quantum algorithms in classical systems.

Contribution

It presents novel noise-based logic algorithms for unsorted database search with exponential speedup and zero error, expanding classical search capabilities.

Findings

Search complexity is O[log(n)] for large databases.

The algorithms have zero error probability.

They outperform quantum search in speed for similar tasks.

Abstract

We explore the collapse of "wavefunction" and the measurement of entanglement in the superpositions of hyperspace vectors in classical physical instantaneous-noise-based logic (INBL). We find both similarities with and major differences from the related properties of quantum systems. Two search algorithms utilizing the observed features are introduced. For the first one we assume an unsorted names database set up by Alice that is a superposition (unknown by Bob) of up to n=2^N strings; those we call names. Bob has access to the superposition wave and to the 2N reference noises of the INBL system of N noise bits. For Bob, to decide if a given name x is included in the superposition, once the search has begun, it takes N switching operations followed by a single measurement of the superposition wave. Thus the time and hardware complexity of the search algorithm is O[log(n)] which indicates an exponential speedup compared to Grover's quantum algorithm in a corresponding setting. An extra advantage is that the error probability of the search is zero. Moreover, the scheme can also check the existence of a fraction of a string, or several separate string fractions embedded in an arbitrarily long, arbitrary string. In the second algorithm, we expand the above scheme to a phonebook with n names and s phone numbers. When the names and numbers have the same bit resolution, once the search has begun, the time and hardware complexity of this search algorithm is O[log(n)]. In the case of one-to-one correspondence between names and phone numbers (n=s), the algorithm offers inverse phonebook search too. The error probability of this search algorithm is also zero.