Analysis of quantum particle automata for solving the density classification problem
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 whether 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.
KeywordsQuantum cellular automata Partitioned cellular automata Quantum particle automata Density classification problem Genetic algorithms Quantum simulation
We would like to thank Dr. David Meyer for his comments and suggestions on this research. We also thank the anonymous reviewers for their comments to improve this paper. Tina also thanks Department of Mathematics at the University of California San Diego for their help during her visit working on this paper.
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