Analysis of Quantum Particle Automata for Solving the Density Classification Problem

TL;DR

This paper explores quantum particle automata for solving the density classification problem, using genetic algorithms to find unitary operators and boundary partitions, demonstrating promising results for small input sizes.

Contribution

Introduces a quantum particle automata approach with genetic algorithms to solve the density classification problem, identifying key parameters influencing evolution dynamics.

Findings

GA found multiple unitary operators for classification

Small θ parameter leads to faster evolution

Results are promising for inputs of length 5

Abstract

To advance our understanding of Quantum Cellular Automata in problem solving through parallel and distributed computing, this research quantized the density classification problem and adopted the Quantum Particle Automata (QPA) to solve the quantized problem. In order to solve this problem, the QPA needed a unitary operator to carry out the QPA evolution and a boundary partition to make the classification decisions. We designed a Genetic Algorithm (GA) to search for the unitary operators and the boundary partitions to classify the density of binary inputs with length 5. The GA was able to find more than one unitary operator that can transform the QPA in ways such that when the particle was measured, it was more likely to collapse to the basis states that were on the correct side of the boundary partition for the QPA to decide if the binary input had majority density 0 or majority density 1. We analyzed these solutions and found that the QPA evolution dynamic was driven by a particular parameter $\theta$ of the unitary operator: a small $\theta$ gave the particle small mass hence fast evolution while large $\theta$ had the opposite effect. While these results are encouraging, scaling these solutions for binary inputs of arbitrary length of $n$ requires additional analysis, which we will investigate in our future work.